The White Sox slugger plans to take some time to figure out whether he feels like playing on, according to the source.
"My goal coming into the season was to give it everything I had in 2013," Konerko told ESPNChicago.com on Monday. "I am going to go at the pace I have been going at; you only get one of these careers. It is not like I have the right answer so I will continue to do what I feel is right."
Konerko's 37-year-old body has suffered through an array of minor aches this season, including a lower back strain that put him on the DL early in the year. He also has sat out 35 games to rest his assorted injuries.
"The last couple of times, and especially in 2005, there was no doubt I would play again," he said. "I understand the inquiries about my future and why people want to know. At the same time, it is still about doing my job; I don't want to get ahead of myself. What is the rush, is the way I feel."
He is expected to address his career in some capacity sometime during the team's last homestand, the source said.
"There are certain things I don't feel obligated to give out [or] tell people," Konerko said Monday. "There are some things that are private, and some people take it the wrong way."
The power numbers certainly have dipped in 2013 for Konerko, who is hitting .248 with 11 home runs and 53 RBIs. His total of 27 extra-base hits in 418 at-bats is the lowest combined number in that category since he started his career with Chicago in 1999.
Konerko is second on the team's all-time list in home runs and RBIs behind former teammate Frank Thomas. He was a free agent in 2005 and 2010, re-signing both times with Chicago.