The 25-year-old has established himself as one of Eredivisie's best midfielders since joining PSV from Heerenveen in January 2022.
The Dutchman has made 115 competitive appearances during his time with PSV, contributing with 22 goals and 40 assists.
Last season, Veerman scored five goals and amassed 16 assists in 29 league matches to help Arne Slot's side lift the Eredivisie title.
Despite being under contract until June 2026, it is currently unclear whether Veerman will remain with PSV beyond the end of the transfer window.
Man United join Veerman race
Veerman has emerged as a potential target for Liverpool, with Slot keen to bring his former player to Anfield this summer.
However, according to journalist Duncan Castles, Liverpool could face competition from their bitter rivals Man United.
The Red Devils have identified Veerman as a potential alternative to Paris Saint-Germian's Manuel Ugarte, who is believed to be their top midfield target.
Man United are understood to be working on a deal for the Uruguayan, but PSG's asking price could scupper their hopes of landing the former Sporting Lisbon man.
Why are Man United searching for a new midfielder?
Whether it's Veerman or Ugarte, it is clear that Man United are determined to add at least one central midfielder to Erik ten Hag's side.
There is currently uncertainty surrounding the Man United futures of Christian Eriksen and Casemiro, while there is a possibility that Scott McTominay could be sold this summer.
The Scotland international has been the subject of bids from London side Fulham, who are looking to bolster their engine room following Joao Palhinha's departure.
McTominay has also been linked with Fenerbahce and Galatasaray, although the latter are set to give up on their pursuit of the Man United man.