The 19-year-old, who was involved in the Portugal squad at Euro 2020, is believed to have attracted the attention of the likes of Man City, Manchester United and Real Madrid over the last 12 months.
According to Record, the Premier League champions have had a £21m offer for the teenager turned down and are now preparing to return with a bid of between £25m and £30m.
The report claims that Sporting want £43m for the left-back, but Man City are not believed to be prepared to meet that figure during this summer's transfer window.
Mendes enjoyed an impressive 2020-21 campaign at club level, contributing one goal and two assists in 35 appearances for the Lions.
The defender still has four years left to run on his contract with the Portuguese champions, but the agreement is thought to include a release clause of £60m.
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