The 20-year-old enjoyed an impressive 2021-22 campaign for his Dutch club, making 43 appearances in all competitions, contributing three goals and two assists in the process.
In the team's title-winning Eredivisie season, he featured on 30 occasions, providing three goals and two assists, while he also appeared eight times in the Champions League this term.
Timber only has little over two years left to run on his current deal, though, and there has been a host of speculation surrounding his future in recent weeks.
Incoming Man United head coach Erik ten Hag is believed to be keen to bring the six-time Netherlands international with him to Old Trafford this summer.
Plettenberg claims that the 20-time English champions are 'seriously interested' in Timber, and discussions with the youngster's management team have already taken place.
When questioned on his future last month, the Dutchman insisted that he was in no rush to leave Ajax, but he spoke of his close relationship with Ten Hag.
"I'm good at Ajax. I can still learn a lot, especially if we continue to play in the Champions League," Timber told Het Parool.
"He deserves it (the Man United job). Ten Hag has been very important to me personally. Under him I became the footballer, the man I am today. The coach talked to me a lot. He's been very critical, in a good, constructive way. I won't forget it any time soon."
Timber spent six years in the Feyenoord youth system before making the move to Ajax, progressing through their various age groups before appearing for the first team in 2019.
The defender has made 74 appearances for the Amsterdam giants in all competitions, contributing four goals and two assists in the process.
Timber has also featured on six occasions for the Netherlands, but he was not part of their squad for the March friendlies with Denmark and Germany due to injury.
The youngster has largely played as a central defender at club level this term but has also operated as a right-back, which are two areas that Man United are believed to be keen to strengthen this summer.
Raphael Varane, Victor Lindelof and Harry Maguire are all expected to be a part of Ten Hag's squad next term, but Phil Jones, Eric Bailly and Axel Tuanzebe could potentially leave in search of pastures new. body check tags ::