Mane has also reportedly been of interest to Manchester United.
Mane has also attracted interest from Manchester United in the past and even made a bid for him in the summer transfer window, according to Sky Sports, though the Mirror's report says that Southampton maintain there were no talks over a possible move to Old Trafford for the 23-year-old and would like to tie him down to a new deal.
The Senegal international has been impressive since his arrival at St Mary's as his pace and end product has caused problems for numerous sides, notably and memorably this season at Stamford Bridge where he tore through the Champions back line to help his side to a 3-1 win in October.
He also scored the quickest hat-trick in the Premier League last season during a 6-1 hammering of Aston Villa in May.
If Southampton were to lose him he would be a big loss, and one would feel if the transfer were to take place than quite a hefty fee would be heading down to the South Coast in exchange.
One would question whether he is the kind of player that Chelsea need right now, as it seems Mane would compete for a place in the area of the field where Jose Mourinho's side are pretty well stocked with the likes of Eden Hazard, Willian and Oscar, even if they have had a very poor start to their campaign.
Despite their win at the weekend, there is definitely a need for some fresh blood at Chelsea in order to take the side forward but given the area of the field that Mane operates in, and the Blues current predicament, it looks more like a move that could happen in the summer rather than this winter, if at all.