And the report claims that although the Saints are preparing for Gallagher to remain at Ewood Park, a 'big January bid' could convince them to change their minds.
Despite Saturday's 4-4 draw against Fulham, Wolves have scored only 25 goals in 20 league matches so far - with Joe Mason (three) their top scoring striker - and Gallagher would surely strengthen Lambert's options.
The England Under-20 international has around 18 months to run on his contract at St. Mary's, and Southampton may look for a quick sale before his value declines.
That said, Charlie Austin's injury lay-off could yet prompt the Saints to exercise their recall option on Gallagher, who also spent time at Milton Keynes Dons.
Austin is expected to miss up to four months with a dislocated shoulder, leaving only Shane Long and Jay Rodriguez as senior strikers.
Wolves have also been linked with a move for Gallagher's Blackburn teammate Ben Marshall, who worked under Lambert in Lancashire and was a reported summer target for the Molineux club.