Forest boss Mark Warburton is said to be seeking an experienced number one, after being left with young pair Jordan Smith and Dimitar Evtimov while Stephen Henderson recovers from injury.
Allan McGregor of Hull City
McGregor fell out of favour at Hull last season, of which he spent the second half on loan to Cardiff City.
But the 35-year-old started the Tigers' opening day draw against Aston Villa, with rival David Marshall potentially sidelined until September.
Nevertheless, he could lose his place again when Marshall returns, and with his contract up next summer anyway, Nottingham Forest are seemingly hoping Hull will waive any transfer fee for the Scotland international.
Hull have already offloaded Eldin Jakupovic to Leicester City, but have another goalkeeper on their books in Will Mannion.
Barrie McKay of Nottingham Forest (left)
Warburton was previously linked with a move for Rangers number one Mark Foderingham (Scottish Sun), having already brought Ibrox winger Barrie McKay to Forest this summer.
Can Nottingham Forest persuade Hull City to free McGregor?