The 22-year-old was in strong form for his Dutch side during the 2021-22 campaign, making 50 appearances in all competitions, contributing one goal and five assists in the process.
Man United were linked with the Netherlands international earlier in the window before their interest seemingly cooled, with Lyon moving into the driving seat for his signature.
However, the 20-time English champions have now agreed a deal with Feyenoord for the left-back, with the club's director Frank Arnesen providing an update on the situation on Tuesday.
"The agreement is there. We are now waiting for Tyrell. If he says yes, then a transfer to Manchester United is imminent," Arnesen told 1908.nl.
Feyenoord will allegedly receive €15m (£12.9m) plus €2m (£1.7m) in add-ons should the deal go through, with Man United in contact with his agents on Wednesday to discuss personal terms.
According to Van der Kraan, a move has now been completed, with his wage demands not proving to be an issue for the 20-time English champions.
"The deal is done, and yesterday he spoke about his own terms," Van der Kraan told De Telegraaf. "They were not so complicated because he already knew what he could earn at Lyon. Manchester United only had to go a little bit over that.
"I think he's going to have a great time there because it's obvious he's a boy who is really made for English football with his dynamism, fierceness, and physical strength despite not being that tall. He really is a top boy.
"You all know that if Manchester United are in the market and you are a footballer, then yes, you go there and not Lyon."
Malacia has spent his entire career at Feyenoord, joining the Dutch outfit's academy at the age of nine in 2008, progressing through their various youth teams before debuting for the first team in December 2017.
The Dutchman has scored four times and registered 10 assists in 136 appearances for his current side in all competitions, winning the KNVB Cup and Johan Cruyff Shield in the process.
The defender also represented Netherlands at Under-16, Under-17, Under-18, Under-20 and Under-21 level before making his senior debut for the national team last September, and he is in a strong position to make the squad for the 2022 World Cup.
Man United currently have three first-team left-backs on their books in the shape of Brandon Williams, Alex Telles and Luke Shaw; the latter is expected to stay at the club this summer, but Williams and Telles could both depart if Malacia arrives.