The Brokeback Mountain star is said to have invited the Friday Night Lights actress on a date last autumn, shortly after she split from New York Yankees player Derek Jeter.
However, Kelly "declined" the request because she "was trying to patch things up" with Jeter, an insider told Us Weekly.
Kelly reunited with Jeter over the holidays. The two were spotted together in Paris on New Year's Eve.
The actress was previously rumoured to have been involved with her Charlie's Angels co-star Ramon Rodriguez.
Watch Minka Kelly in the trailer for Searching for Sonny below: