The 22-year-old spent the second half of the 2023-24 campaign on loan at Borussia Dortmund, making 23 appearances for the German giants, scoring three times and registering two assists in the process.
Maatsen is due back at Stamford Bridge this summer, and he has a contract with the London giants until the end of the 2025-26 campaign, with the deal said to include a release clause of £35m.
Villa and Chelsea are expected to do business this summer, with the latter said to be keen on Jhon Duran, while the former are thought to want Conor Gallagher.
According to Sky Sports News, Villa have also been in talks with the Blues over the possibility of bringing Maatsen to Villa Park this summer.
The report claims that Dortmund are also keen on a permanent deal, with Chelsea thus far pointing to the release clause when it comes to their valuation of the left-back.
Rangers 'to step up interest in Barron'
Meanwhile, Rangers are allegedly keen to bring Aberdeen midfielder Connor Barron to the club this summer.
The 21-year-old only has a contract with his current side until the end of the month, and he is widely expected to move on ahead of the 2024-25 campaign.
According to The Scottish Sun, Rangers have stepped up their interest in Barron, with the Gers currently at the head of the queue for his services.
The report claims that Cagliari are leading the Italian interest, while there are also a number of clubs in England that have made it clear they want to sign him.
Swansea City and Middlesbrough are named as potential candidates for his signature, and Aberdeen will be due a compensation fee if he does not sign a new deal.
Barron, who has been capped by Scotland Under-21s, has represented his current side on 76 occasions in all competitions, contributing two goals and five assists in the process.
Southampton 'lead the race for Ghoddos'
Elsewhere, Southampton are allegedly leading the race to sign Saman Ghoddos on a free transfer.
The 30-year-old's Brentford contract is due to expire at the end of the month, and he is widely expected to leave the Bees.
A number of clubs have been credited with an interest in the attacker, who has scored three times in 53 caps for Iran.
However, according to Varzesh Se, Southampton are firmly at the head of the queue for his signature, with Saints widely expected to confirm his arrival at the start of next month.
The report claims that Ghoddos is determined to continue his career in English football, and personal terms between the two parties have already been agreed.
Ghoddos featured on 20 occasions for Brentford during the 2023-24 campaign, including 19 appearances in the Premier League, finding the back of the net against Burnley back in October.