The Dons were keen on bringing the midfielder to the club in January but were reluctant to pay £175,000.
The 26-year-old will have 12 months to run on his deal in the summer and could be one of a number of key figures to leave the Tony Macaroni Arena.
Declan Gallagher and Craig Halkett are both out of contract and been linked with moves to Motherwell and Hearts respectively.
Pittman, who signed a new deal ahead of the start of this season, has made 36 appearances in all competitions so far this campaign, netting six times.
He joined the club in February 2015 having been playing in the Juniors and has played in League One, the Championship and now the top tier.
Aberdeen see him as a potential replacement for captain Graeme Shinnie who, along with Gary Mackay-Steven, is out of contract at the end of the season.