Glazer, whose family have been in control of United since he became owner in 2005, passed away on Wednesday at the age of 85.
His tenure with the Red Devils had been an uneasy one, with many United fans unhappy at the level of debt his takeover had put on the club, although the team have largely continued to prosper.
A statement from the Barclays Premier League outfit on Wednesday said ''the thoughts of everyone" at United were with the Glazer family, to whom the staff extended "deep and sincere condolences".
And on Thursday morning, a message appeared on Holland international Van Persie's official Twitter account which said: "My condolences go out to the Glazer family and friends."
The news Glazer had died was announced by the Tampa Bay Buccaneers, the National Football League (NFL) franchise he took over in 1995.
The Buccaneers went on to achieve seven play-off berths, five play-off victories and their only Super Bowl triumph, which came 12 years ago.
A host of tributes have been paid to Glazer by figures connected with the Tampa Bay franchise and from within the wider NFL community.
Jon Gruden, who was head coach at the time of the Super Bowl triumph, said: "He was a friend and a trailblazer
I'll miss him and I thank him for believing in me.
"My condolences to the Glazer family and to the Bucs organisation."
Tony Dungy, Gruden's predecessor, wrote on Twitter: "A very sad day for me learning of passing of Malcolm Glazer.
"He was special in my life
I loved the family atmosphere he set for the Bucs."
Former players who were involved in the Buccaneers' Super Bowl success also took to Twitter to leave messages.
Warren Sapp said "one time for my owner & great man #RipBoss", while Derrick Brooks wrote: "Deeply saddened by passing of Mr Glazer.
"So many good memories of him as my owner of the only team I played for @TBBuccaneers
#ripmrglazer"
Current Tampa Bay players had their say as well.
Defensive end Da'Quan Bowers wrote: "RIP TO MALCOM GLAZER, a man and family that gave me an opportunity to live out a dream and has been in my corner since DAY 1 RIP BOSSMAN."
Tributes also came from some of Glazer's fellow franchise owners.
Miami Dolphins owner Stephen Ross said in a statement: "I was deeply saddened to hear about the passing of Malcolm Glazer.
"He was a Super Bowl champion, a true innovator and pioneer that cared about his family, the community and his team."
New England Patriots owner Robert Kraft said: "Malcolm Glazer was a very good man who I admired
He was known as a great businessman
He made everything he ever invested in better, including his community, where he invested in many philanthropic endeavours.
"I was always inspired by his love and devotion to his wife, Linda, and his commitment to his family
He was so proud of his children, Avie, Kevin, Bryan, Joel, Darcie and Edward
I loved that he always put his family first.
"I offer my sincerest sympathies to Linda, his six children and 14 grandchildren, as well as the many friends and extended family who are mourning his loss today
He will be missed dearly."
The Buccaneers have announced a private family funeral service will be held in due course.
Source : PA
Source: PA