Ipswich Town had been chasing the 26-year-old Northern Ireland international but The Bolton News understands he has discussed a deal with the Whites, contingent on the Football Ventures takeover going ahead.
Thompson made more than 100 appearances for Southend United, helping Phil Brown’s side to promotion from League Two.
He repeated the feat at Gigg Lane last season under Ryan Lowe but walked away from the club this summer after pay issues.
Wanderers have experienced their own troubles on that front but with hopes high that the club can be sold in the next couple of days, some trialists have been brought into the camp ahead of a behind-closed-doors friendly against Bradford City.
Winger Craig Conway, formerly of Blackburn Rovers, and striker Billy Clarke – who played at Bradford last season – have been working with the squad.
Defenders Jack Hobbs and David Wheater were also training at Lostock, having had their Bolton contract expire at the end of last season.