Town chief David Wagner remains keen on keeping the 24-year-old, but the former Kidderminster player is desperate to play regular football, something that several Championship sides are willing to offer him.
Linking up with the club he supported as a boy in Villa is also likely to prove an enticising factor for Lolley.
Johan Djourou’s proposed move to Sheffield Wednesday has fallen through.
Talks have since broken down between the two parties and it is unclear whether the deal will be resurrected.
Djourou, capped 67 times by Switzerland, is a free agent after leaving Hamburg at the end of last season.
The 30-year-old spent a decade with Arsenal, making 140 appearances including 19 in the Champions League.
Aden Flint was left out of Bristol City’s opening day win over Barnsley as the speculation over his future intensifies.
A target of Birmingham City and also linked with Middlesbrough earlier this summer, Flint was a substitute as the Robins ran out comfortable 3-1 winners over the Reds.
Flint did appear from the bench in the 82nd minute, but the fact that one of last season’s key performers was left out of the starting line-up at Ashton Gate will raise questions over the centre-back’s future.
Bristol City rejected a double bid from Birmingham for Flint and teammate Joe Bryan last week after receiving an offer that manager Lee Johnson described as “derisory” .
Leeds were linked with Flint last month, but it is thought that he is not a target that the club are actively pursuing.