The Wales internationalist, who joined Celtic on a Bosman transfer from Cardiff City in 2011, has two years left on his contract, but with Celtic's Champions League involvement unlikely to extend beyond the preliminary stages (they are 4-1 down to Legia Warsaw after the first leg in Poland last week), the champions could be willing to make up some of the financial shortfall by selling the defender.
A full-back is high on the priority list for Gary Monks, the Swansea manager, but the asking price
for his preferred target, Tottenham Hotspur's Kyle Naughton, is proving prohibitive, and he could now turn to Matthews.
A second-string Celtic side went down 6-1 to Tottenham in Helsinki at the weekend and the organisers of the match are reported to be seeking an apology and a refund from Ronny Deila's side after saying the decision to send a young inexperienced team as 'disrespectful'.
Faced with overturning the 4-1 Champions League first-leg deficit to Legia on Wednesday, Deila and his first team stayed in Glasgow as a development squad travelled to Finland. Efe Ambrose, Teemu Pukki, Amido Balde and Craig Gordon were the only senior
first-team players involved.
Celtic defended the move by saying Deila had inherited the game from the previous management team.
Ambrose, who was sent off during Saturday's match - his second dismissal in 72 hours - will not face a ban. The Nigerian was dismissed when he was given a second yellow card after a last-minute challenge on Emmanuel Adebayor.
He had been booked seven minutes beforehand for a foul on the same player, then needlessly hauled down Danny Rose with a couple of minutes to go to give Tottenham a penalty.
It appears Finnish referee Antti Munukka will not include the sending-off in his report to the Finnish FA as the match was a friendly.
Ambrose had been sent off in the first half of Celtic's visit to Warsaw last week.