The Red Devils were handed a boost in the summer when Real Madrid signed Thibaut Courtois from Chelsea FC to provide Keylor Navas with competition.
The Manchester United goalkeeper has been regularly linked with a move to Real Madrid over the past four seasons at Old Trafford.
De Gea has established himself as the Premier League’s standout goalkeeper over the past four seasons.
The 27-year-old has 24 months left to run on his current deal with the 20-time English champions.
Former Liverpool FC and Manchester City striker Bellamy urged Manchester United to resolve De Gea’s contractual situation.
“He has to [re-sign]. Man United have to get it done,” Bellamy told Sky Sports. “They are taking their time a little bit because Courtois went to Real Madrid.”
De Gea moved to Manchester United in a £17m deal from La Liga side Atletico Madrid in the 2011 summer transfer window during Sir Alex Ferguson’s spell in charge.
The Spanish goalkeeper has won the Premier League title, the Europa League, the FA Cup and the League Cup during his spell at Old Trafford.
Manchester United played out a goalless draw with promoted side Wolverhampton Wanderers in the Premier League at Old Trafford last weekend.
The Red Devils finished in second spot in the Premier League table last term.
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