The Red Devils allowed David de Gea to leave the club on a free transfer last year and then brought in Onana as his replacement, with the Cameroonian arriving from Inter Milan.
The 28-year-old has had a difficult first season at Old Trafford, conceding 79 times in 47 appearances in all competitions, keeping only 12 clean sheets in the process.
Onana has again faced criticism for his display against Crystal Palace on Monday evening, with the 20-time English champions conceding four unanswered goals at Selhurst Park.
The stopper has another four years left to run on his contract, but there have been claims that the club could target a new goalkeeper this summer, with Sir Jim Ratcliffe, who has taken over the football department at Old Trafford, planning major changes in a bid to help the club return to former glories.
Man United 'keen on Real Sociedad goalkeeper Alex Remiro'
According to Marca, Man United are huge admirers of Remiro, with the Red Devils viewing him as a possible replacement for Onana during the upcoming market.
The report claims that Real Sociedad are not willing to allow their number one to leave for less than his €70m (£60m) release clause, but the Red Devils are hopeful that they will be able to negotiate.
Remiro came through the youth system at Athletic Bilbao and turned out for the Basque outfit's second team between 2014 and 2016.
The Spaniard failed to make the breakthrough into the first team, though, and following loan spells with Levante and Huesca, he left for Real Sociedad in the summer of 2019.
Remiro has made 217 appearances for his current side in all competitions, conceding 207 times and keeping 93 clean sheets in the process.
Would Alex Remiro be a good signing for Man United?
The goalkeeper has been in strong form for Real Sociedad during the 2023-24 campaign, keeping 20 clean sheets in 40 appearances in all competitions, including 14 in 32 La Liga matches.
Remiro was also excellent in the Champions League this season, keeping clean sheets in four of his eight matches, conceding only six times.
Real Sociedad have the Spain international on a contract until June 2027, and the presence of a sizeable release clause has placed them in a strong position when it comes to his future.
At €70m (£60m), it would be a risk for Man United, as there are so many other areas in the squad that need to be strengthened during a hugely important transfer window.
Onana has found it difficult this season, though, and Remiro certainly has the credentials to perform for Man United, with the team desperately needing a dependable performer between the sticks.