The World Cup winner is being touted as a potential United target, although manager Louis van Gaal is remaining tight-lipped on the increasing speculation.
When I signed there were five centre-backs who I had to work hard to get past
Smalling managed to make 25 Premier League appearances last season despite increased competition for a starting spot from Daley Blind and Marcos Rojo.
The former Fulham defender insisted that he would be up for the challenge of competing with the Madrid centre-half if Ramos sealed a moved to Old Trafford.
“I think it’s a case of at Manchester Untied there’s always competition,” Smalling is quoted as saying by Sky Sports.
“Even when I signed there were five centre-backs who I had to work hard to get past, so I always knew I was going to be compared against the best because United can always challenge for the best, and I’m up for that challenge.”
Smalling, who signed a four-year deal with the Red Devils earlier this year, scored four goals in 29 games in all competitions last season.
The England international has won two Premier league titles following his reported £10m move from Fulham in 2010.
The 6ft 3ins defender has established himself as a regular Three Lions international during his spell at United.
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