The England left-back will be available on a free at the end of the season, and has been linked with a move to Premier League rivals Manchester United.
However, The Sun reports that the 31-year-old's mum let slip her son's future club on Facebook, posting: "Well looks like his going somwhere better hear than the talk of man u. Not too far on the Euro star x”
Mrs Cole added a link to a news report linking Ashley to the Qatar-owned Ligue 1 side.
Chelsea are preparing a sensational £30 million bid for Everton midfielder Marouane Fellaini, according to the Sunday People.
The Belgian has been in sparkling form this season, underlining his quality with a goal and an assist against Sunderland on Saturday.
Roberto Di Matteo sees the marauding Belgian as the ideal replacement for Frank Lampard, and has reportedly been given the green light to tempt cash-strapped Everton with a huge bid.
Fellaini is seen as the ideal mid-season acquisition as he would be eligible for the knock-out stages of the Champions League.
Regular readers of Paper Round may have noticed two names cropping up more than any others over the last year - Radamel Falcao and Edinson Cavani.
The South American pair - arguably the two best players outside Europe's established giants - are in high demand, and both could be Premier League-bound according to this morning's reports.
Let's start with Napoli striker Cavani, whom the Mail on Sunday claims is the subject of Arsenal's affections.
After a rocky start to the season and a tempestuous club AGM, Arsene Wenger knows the fans are no longer prepared to wait for success and is readying a £30m January bid for the Uruguayan.
The MoS claims Wenger received a glowing report on Cavani from his chief scout Steve Rowley who saw him score all four goals in a 4-2 Europa League win against Dnipro Dnipropetrovsk - though, frankly, anyone with a satellite TV subscription could tell you Cavani is the real deal.
The 25-year-old will not come cheap, though. Earlier this year he signed a five-year contract with Napoli, putting both he and his club in a strong bargaining position
On to Falcao, whom the Daily Star Sunday claims Manchester City have targeted.
Manager Roberto Mancini held his first meeting with new director of football Txiki Begiristain this week, and the pair have reportedly earmarked Atletico Madrid striker Falcao as their main attacking target.
Again, this is a conclusion anyone with a TV and a pair of eyes could have reached, but that's football.
The Sunday Telegraph also chips in, claiming City have already met with the Colombian's representatives.
Falcao recently scored 13 goals in eight games, including a hat-trick against Chelsea in the UEFA Super Cup, and has a £45m buy-out clause in his contract.
If City get their man, they will sell Edin Dzeko to partially balance the books - Chelsea, Liverpool and a host of overseas clubs are among those interested in the Bosnian.