Manchester United had explored the possibility of signing Maatsen towards the end of the summer transfer window, as they searched for reinforcements at left-back to compete with Luke Shaw, having failed in a separate pursuit of Newcastle's Lewis Hall.
Aston Villa, though, were never willing to let their man leave and rejected any approach for the 24-year-old before the deadline passed, regarding him as one of their key performers under Unai Emery this season.
Sky Sports reported at the time that Aston Villa had already lined up a new contract offer, and Fabrizio Romano has since confirmed there are "no doors open" for any deal involving United this year or beyond.
Now, negotiations over that contract extension for Maatsen are progressing well, with Villa keen to reward his performances by tying him down on improved terms and removing any transfer speculation heading into the winter window.
His current deal runs until June 2030, but the plan is to extend that further and increase his salary at Villa Park to reflect his standing in the squad and his importance to Emery's plans going forward.
The Netherlands international has become a key figure for Emery, starting all five of Villa's matches so far this season and establishing himself as first choice at left-back ahead of alternatives in the squad.
Villa have made a mixed start to the campaign under Emery, but Maatsen's form has been one of the more encouraging aspects of their opening weeks across the Premier League and cup competitions this season.
The Dutchman joined Villa from Chelsea for a fee of around £37.5 million and has continued to develop into one of the more reliable full-backs in the Premier League, a factor behind United's interest before the deadline closed.
Maatsen has also earned senior international recognition with the Netherlands, and his development at club level has not gone unnoticed elsewhere in Europe.
Aston Villa's stance throughout the swirl of transfer talk was clear: Maatsen was not for sale, and the new contract being discussed is designed to remove any lingering uncertainty over his long-term future at Villa Park.