Wolves' Lonergan is said to be seeking a move north, and Hull may be willing to oblige.
Hull sold Eldin Jakupovic to Leicester City last month and could have David Marshall sidelined for much of August.
Allan McGregor started the Tigers' opening day draw at Aston Villa, however, the 35-year-old is said to be attracting interest from Nottingham Forest (The Sun on Sunday).
Allan McGregor of Hull City
McGregor was out of favour at Hull last season, of which he spent the second half on loan to Cardiff City, and could fall back down the pecking order once Marshall returns.
With youngster Will Mannion the Yorkshire side's only other option between the sticks, another more experienced option may be required if McGregor is allowed to leave - and Lonergan could be that man.
The 33-year-old was reportedly told he can leave Wolves this summer (Express & Star) and wasn't even on the bench as Nuno Espirito Santo's side beat Middlesbrough on Saturday - even with Carl Ikeme sidelined.
Nevertheless, he is a veteran of more than 300 Championship appearances and could be a cost-effective signing for Hull, given his contract expires at the end of the current campaign.
Andy Lonergan of Wolverhampton Wanderers
It is claimed that Preston-native Lonergan is looking to leave Wolves to be 'closer to his northern base'.
Should Hull move for the Wolverhampton Wanderers man?