And Vargas -- as most free agents tend to do -- opted to wait out the five-day exclusive negotiating window to delve into a thin free-agent class of starters, all of whom were free to talk with other teams as of 9:01 p.m. PT on Monday.
"We obviously have interest in having Jason back," Angels general manager Jerry Dipoto said when reached by phone Monday night, though he opted not to go into further details. "This is the process and it's playing itself out, and we'll honor that. Obviously Jason earned the right to see what was out there in free agency. We'll maintain a rhetoric with him and do have interest in him returning. I think it's a mutual interest."
In the end, it may come down to one element: the third year.
MLBTradeRumors.com predicted a three-year, $28.5 million contract for Vargas. But the Angels are hesitant to go a third year and at this point don't seem willing to approach an average annual value of $10 million with the 30-year-old left-hander, considering he projects as a fourth starter in their rotation.
Vargas will no doubt hold out for something better. But keep in mind that just last season, only five starting pitchers -- Zack Greinke, Anibal Sanchez, Edwin Jackson, Kyle Lohse and Jeremy Guthrie -- garnered deals longer that two years. And while Vargas has been a steady mid-rotation starter over the last four seasons, he isn't considered among the top handful of available arms despite a thin free-agent class.
The Angels didn't tender Vargas the one-year, $14.1 million qualifying offer because there was little doubt in their mind that he would accept it, and they'd be too close to the luxury-tax threshold if he did.
The Angels have $126.5 million committed for next season. That figure includes the $18.6 million they owe the Yankees for Vernon Wells' final season, but doesn't include contracts for players with zero to three years of service time and up to eight potential arbitration cases (for Peter Bourjos, Ernesto Frieri, Juan Gutierrez, Tommy Hanson, Kevin Jepsen, Chris Nelson, Mark Trumbo and Jerome Williams ).
A rough projection of the Angels' current Competitive Balance Tax payroll for 2014 -- calculated as the average annual value of all 40-man-roster contracts, plus benefits -- is $175 million, or $14 million shy of the threshold at which teams will be taxed 17.5 percent for going over for the first time next season.
The Angels, like most others, don't want to venture into that territory. But they would also like to find a way to work out an affordable long-term deal with Vargas, who has averaged 10 wins, a 3.97 ERA and 190 innings over the last four years.
Vargas, acquired from the Mariners in a trade for Kendrys Morales last Dec. 19, went 9-8 with a 4.02 ERA in 150 innings during a 2013 season that saw him miss nearly two months because of a blood clot in his left armpit area.
Vargas was born and raised in Southern California, briefly attended Long Beach State with Jered Weaver -- whom he's still good friends with -- and is confident that the Angels have the talent to be a competitive team in 2014, regardless of how this past season turned out.
"It was good, I enjoyed it," Vargas said of his first season in Anaheim. "I wish I wouldn't have had to have surgery, but those are just things that happen. Everything else, it was great. And my family had a great time. I really enjoyed it."
Now, Vargas joins a free-agent class that, in the words of one executive, "is pretty terrible."
Only three starting pitchers -- Ervin Santana, Ubaldo Jimenez and Hiroki Kuroda -- received qualifying offers and none of the arms currently available are considered bona-fide aces, which could play right into Vargas' hands.
If Vargas re-signs, he'll join a rotation trio that includes Weaver, C.J. Wilson and Garrett Richards. But the Angels would still look to bolster a staff that finished 11th in the American League in ERA via trade, by dangling offensive pieces -- like Trumbo, Erick Aybar, Howie Kendrick and Bourjos -- in hopes of prying away cost-controlled arms.
The wild card, though, is Masahiro Tanaka, the 25-year-old Japanese right-hander who went 24-0 with a 1.27 ERA in 212 innings for the Tohoku Rakuten Golden Eagles of Nippon Professional Baseball.
The Angels have scouted Tanaka multiple times and would be among many interested teams if he gets posted, even though he's expected to exceed the contract Yu Darvish got from the Rangers two offseasons ago.
The reason is simple: Tanaka would easily be the best free-agent starter available and, under the current posting-system agreement, his contract wouldn't count toward a team's luxury tax threshold. (Darvish, for example, costs the Rangers less than $10 million per year toward the CBT because his $51.7 million posting fee isn't included.)
For now, though, the Angels will keep tabs on Vargas, hope for a generous trade market and, perhaps when things start to dry up, turn another eye toward free agency, where several low-risk, high-reward deals -- Roy Halladay, Josh Johnson and Johan Santana are among several intriguing names -- may eventually make sense.
"There's a number of starters out there that we have interest in on some level," Dipoto said, "but right now our priority is focusing on Jason."