O'Shea joined the Spireites on loan in late November and impressed during his stay at the Proact Stadium.
The 24-year-old Irishman capped his final appearance for the npower League Two club on Saturday with a goal - the second during his stint in north east Derbyshire - but it was not enough to prevent Paul Cook's side from losing 2-1 at Wycombe.
Chesterfield chief executive Chris Turner told his club's official website: "He scored a good goal on Saturday and hit the crossbar, and was unlucky not to score a few more goals in his spell here.
"Paul's [Cook] intimated that he wants to sign him and we'll try our best to come up with something this week if possible."
Meanwhile, transfer-listed striker Craig Westcarr has returned from his loan spell at Walsall. But Turner revealed the 27-year-old could be on his way back to the League One club.
He said: "I'm led to believe that Walsall want to offer him a deal until the end of the season, so we are working on a deal around that."