Pedroia is discussing options with his family, agents, and the Red Sox, Abraham adds.
The 36-year-old has appeared in just nine games over the past two seasons due to continued knee issues. Pedroia was attempting to recover from a joint preservation procedure he underwent in August.
Although Pedroia's recovery appeared to be going well before this setback, the veteran infielder sounded cautious about playing in 2020.
"I spent two years saying I was going to come back and kick everybody's ass and then I played nine games," Pedroia said during a November interview on the BradFo Sho Podcast. "It is what it is."
"You have to find a way to deal with it the best way you can," he added. "I'm not going to sit here and say I'm going to come back and be better than ever. Could I? Maybe. I don't put it past anybody."
Over 14 seasons with the Red Sox, Pedroia owns a .299/.365/.439 slash line with 140 home runs and 725 RBIs.
He was the American League Rookie of the Year in 2007, won an AL MVP the following season, and has earned four Gold Gloves.
Pedroia was also part of the Red Sox when they won World Series titles in 2007, 2013, and 2018.