The Ghanian international has just four months left on his current contract with the French side and the Swans are hoping to steal a march on their competitiors and secure his signature.
Mensah, who has won 36 caps for Ghana, is enjoying the most successful spell of his career at Evian, but was banned for four months in May by FIFA for breaching contract after it emerged that he was still contracted at Italian club Udinese when he claimed to be a free agent.
The report claims that Swansea have been scouting the 25-year-old regularly with a view to making a move for him and that they will act upon this at the end of the season.
Guidolin will be keen to bolster his defensive ranks in a bid to prevent a repeat of this season, in which the club have struggled for consistency under the Italian and his predecessor, Garry Monk.
The Swans are 16th in the Premier League table, just three points clear of the relegation zone.
They face a tricky few weeks of fixtures, with consecutive trips to North London to face high-flying Tottenham Hotspur and Arsenal as their next two matches.