Burgess has spent much of the last 12 months on loan from Ewood Park, firstly Down Under with Northern Spirit and this season with Second Division promotion-chasers Brentford.
The bustling frontman could provide McMahon with a fresh option in the Seasiders team, perfectly replacing Brett Ormerod who was sold to Southampton earlier this season.
Blackpool have confirmed that they are indeed seeking new recruits over the summer, but would not be drawn on the identity of any targets.
"Steve wouldn't reveal names of players he's looking to bring in - he never does. But certainly he's made clear that he will bring in new faces over the summer." revealved one source.
Several out-of-favour Seasiders will be offloaded during the close season, increasing the plausibility of them making a swoop for 20-year-old Burgess.
McMahon and Souness have already dealt with each other this season following Darren Dunning's loan switch to Bloomfield Road.