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Two teams previously linked to Encarnacion in the rumor mill have already filled their open spots at DH, with the Astros signing Carlos Beltran and the Yankees agreeing to terms with Matt Holliday.
Fox Sports' Ken Rosenthal reported Monday that Houston could theoretically still sign Encarnacion and play him mostly at first base, where he played 75 games last year.
The Red Sox, long thought to make a push for Encarnacion, don't appear to be as interested as reports initially speculated. His former team, the Blue Jays, already signed Kendrys Morales and on Monday inked utility man Steve Pearce to a two-year deal.
• Rangers, Indians connected to Encarnacion
Encarnacion spoke with his agent, Paul Kinzer, following Pearce's signing and expressed disappointment in not being able to return to Toronto, Kinzer told MLB.com's Jon Morosi.
"Edwin loved Toronto. He hoped to go back," Kinzer said. "But he waited his whole career for free agency and wanted to see what's out there."
The Blue Jays made a four-year, $80-million offer to Encarnacion during the quiet period, but Encarnacion wanted to explore offers with other clubs, Kinzer told Morosi.
Several factors appear to be working against Encarnacion, including his attachment to a Draft pick and a glut of first base/designated hitter-types on the market. Encarnacion certainly ranks at the top the list, however, as he is second in home runs and second in RBIs among all Major Leaguers over the past five seasons.
Encarnacion, who turns 34 in January, is coming off a season in which he hit .263 with 42 home runs and 127 RBIs in 160 games. He is thought to be looking for a four- or five-year deal, though he could take a shorter deal with a higher average annual value.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.