The 23-year-old only joined Sheffield United in a big-money move from Bournemouth last August, but the club's relegation to the Championship has led to speculation surrounding the stopper's future.
Ramsdale conceded 63 Premier League goals during the 2020-21 campaign, but he was named on England's standby list for Euro 2020 and has been linked with an immediate return to the top flight, with Wolverhampton Wanderers thought to be admirers.
According to the Daily Mail, Spurs are also considering an approach for the goalkeeper, as the North London club prepare for life after Hugo Lloris.
The France international only has 12 months left to run on his contract at the Tottenham Hotspur Stadium and is thought to be a target for Paris Saint-Germain.
Tottenham are yet to announce a new head coach, but the club are allegedly in talks with former Roma boss Paulo Fonseca, having seen talks with Antonio Conte break down.