Connolly is looking for a new club after being released by Leeds earlier this summer.
The 29-year-old had a spell on loan at Preston in the second half of last season, making 15 appearances for the League One outfit.
Connolly moved to Elland Road from Derby County in the summer of 2010, having also had stints with Sheffield United and Plymouth Argyle earlier in his career.
MLS side New York Red Bulls are now hoping to lure the full-back to America where he could link up with former Arsenal hero Thierry Henry.
A number of English clubs are also keeping tabs on Connolly's situation and the player is mulling over his future options, according to Sky Sports.