Hart will be out of action for around two weeks after injuring his ankle in a Premier League match at Hull last weekend.
With the club's third-choice custodian Richard Martin also injured, manager Mark Hughes has been granted permission by the Premier League to bring in a goalkeeper on loan.
Hedman, 35, claims he has been approached by City but he has turned them down as he fears he is not in the right condition.
"They want me to sit on the bench for this weekend's game (against Arsenal), but I need at least two weeks' training," Hedman told sportbladet.se.
"But my answer of no is not definitive. I need to think about it further."
Kasper Schmeichel is set to be City's goalkeeper against the Gunners at Eastlands on Saturday, with 18-year-old Norwegian Tobias Johansen the only fit back-up on the books.
Hedman, who played for Coventry between 1997 and 2002, spent a short period on loan at Chelsea in November 2006 but did not make a first-team appearance.
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