The Dutchman has had a difficult 2020-21 campaign with the Red Devils since his £40m arrival last summer from Ajax.
Van de Beek, who was ruled out of Euro 2020 with an injury, is believed to be considering his future at Old Trafford, although Ole Gunnar Solskjaer is not looking to offload him this summer.
According to football journalist Fabrizio Romano, the Gunners are hoping to sign a midfielder in this summer's transfer window, however they have not yet held talks with the 24-year-old.
Buendia has since left Norwich City and joined Aston Villa for a club-record fee, while Odegaard's future at the Santiago Bernabeu remains uncertain.
Van de Beek featured 36 times across all competitions for United last season, but he only started four times in the Premier League. body check tags ::