West Ham United are linked to the Portugal international.
West Ham are strongly linked with the Sporting Lisbon midfielder, who was the subject of a £27.1 million bid today, as reported by the same publication.
And The Mail reports that the Portugal international would be rewarded with a £100,000-a-week deal if he signs for Slaven Bilic's side this month.
Sporting are said to be holding out for around £39 million for one of their prized assets, who has been heavily linked with a move to Arsenal over the past three years.
West Ham have had an excellent window thus far and Carvalho would be joining Pablo Zabaleta, Joe Hart, Javier Hernandez and Marko Arnuatovic as Bilic's summer recruits.
According to The Mirror, Hernandez was demanding £140,000 per week prior to officially joining, but it remains to be seen what he is earning, and The Sun claimed that their club-record signing Arnautovic, who joined for £24 million, is their highest earner.
The Irons kick off the Premier League season with a trip to Manchester United on Sunday.