Mahon, 31, is looking for a new club after being released by the Clarets earlier this summer.
Tranmere boss John Barnes has invited the Republic of Ireland international to join them for pre-season training so that he can have a look at him.
If Mahon impresses during training he could win a move back to the League One outfit.
Mahon started his career at Tranmere, spending five years at the club before joining Sporting Lisbon, and made more than 60 league appearances for Burnley, scoring four times.
Coca Cola League 1 Promotion 2009/10 Win Outright: Tranmere 8/1