The right-hander is rehabbing from arthroscopic surgery on his left knee to repair a torn meniscus. He was placed on the disabled list Aug. 11 and projected to be sidelined four to six weeks.
"He's definitely pushing a little bit," Cubs manager Joe Maddon said of Strop.
John Lackey, sidelined since Aug. 15 with a right shoulder strain, also threw a bullpen session Monday, while Hector Rondon continues to make progress. Rondon is rehabbing a strained right triceps.
"We're trying to play it smart and not push them too quickly," Maddon said.
Lackey will need at least one more bullpen before he can be inserted into the rotation.
• Cubs president of baseball operations Theo Epstein said he and the rest of the front office were discussing possible callups for when rosters expand on Thursday. Maddon said whoever is added will be "pertinent people who can help" the team win.
Epstein said they also have talked about the possibility of switching to a six-man rotation in an effort to conserve the starting pitchers. One option would be to keep lefty Mike Montgomery in the mix; he's been subbing for Lackey and will make his third start for the Cubs on Wednesday.
• Addison Russell did not start Monday, part of Maddon's plan to keep players fresh. The shortstop went 8-for-37 on the nine-game road trip, hitting five home runs and a double, and driving in 10 runs. He has at least one RBI in nine of his last 12 games.
"I'm just trying to be proactive and give guys days off," Maddon said.
• Carl Edwards Jr. had what Maddon likes to call a "big boy moment" on Sunday when the rookie reliever was called on in the Dodgers' eighth with the bases loaded and one out. First up for Edwards was Justin Turner, and the right-hander said he was hoping to get a double play. Instead, Edwards struck Turner out on a 97-mph fastball.
Next was Adrian Gonzalez, and Edwards got the ground ball he wanted as Gonzalez hit it to third baseman Javier Baez. But Baez threw to second baseman Ben Zobrist, who had to run because he was playing deeper because of a shift, and the two could not get an out, enabling a run to score.
"I told Javy, I'm like, 'Bro, it happens, it's OK,'" Edwards said Monday. "I know we wanted to win and it's a crucial time, but at the end of the day, we got out of there without giving up the house, we just gave up one and still had a chance to win that game. It was another one of those big boy moments."
Maddon keeps testing Edwards in such situations.
"To come in after the intentional walk, to have the bases loaded, to face those two guys, I feel my confidence was [high]," Edwards said.
• The Cubs and the Myrtle Beach Pelicans signed a four-year extension of their Player Development Contract. The agreement will keep the Pelicans as the Class A Advanced affiliate through the 2020 season. Myrtle Beach players from the 2015 and '16 seasons make up five of the top eight, and 12 of the top 30 prospects in the Cubs organization, according to MLBPipeline.com.