O Jogo have stated that the midfielder is still holding out hope for a move to the Premier League.
As such, Arsene Wenger may well look to bolster other positions in the transfer market instead of the centre of the park this summer.
The Portugal international has impressed over the last 18 months with solid performances for club and country.
The report states that although interest in him appears to have waned in recent months, the star is still hoping for a move to Arsenal or Manchester United at the end of the current campaign.
With the likes of Coquelin, Mikel Arteta, Jack Wilshere, Santi Cazorla and Aaron Ramsey in contention for starting berths in the heart of the North London club’s midfield, it remains to be seen whether Carvalho will get his dream move or not this summer.
After representing his nation at last summer’s World Cup, the 23-year-old has started 25 Primeira Liga games this season, scoring one goal.