The England defender and his club colleagues returned for pre-season training on Monday.
And James Wilson, who has five caps for the Young Lions at U20 level, had indicated on the club’s website that GPS tests found centre-back Smalling to be United’s quickest player.
Smalling and Phil Jones in FATV's 'Room-mates'
Speaking to ManUtd.com, Smalling believes no-one in the Red Devils playing staff would be keen to go up against him in a race.
"I would back myself against the majority, whether it be over five, 10 or 40 metres," said the former Fulham defender who has played 18 times for the Three Lions.
"That might surprise a few people but I think, if you ask most of the lads, they wouldn't want to race me!"
Revealing who he thought would be a potential challenger, he added: "Willo [James Wilson], Angel [Di Maria] and probably Youngy [Ashley Young]. We're the speedsters!"
Throwing down the gauntlet, he finished with a challenge.
"We haven't really had a race. When we warm up, we do five or 10-metre sprints but they're generally in fours or fives so it's not an actual race.
"But hopefully, come pre-season, we can have one – I'm game for that!"
