Both Premier League sides could well do with fresh central midfield options and the lack of a signing of this type over the summer may well have left both clubs well short of mounting a genuine Premier League title challenge.
Arsene Wenger opted to trust to Francis Coquelin following the French utility man’s fine displays over the course of the second half of 2014/15, however in doing so the Arsenal manager has placed far too much of a risk on the player, who he was after all happy to loan out to Championship side Charlton Athletic last term.
Back-up options Mikel Arteta and Mathieu Flamini are both past it and if Coquelin were to suffer an injury or a drop in form then Arsenal would be in trouble.
Brendan Rodgers is similarly stretched due to injuries suffered by both Jordan Henderson and Joe Allen and Brazilian Lucas Leiva, who looked likely to leave over the summer, has now found himself back in favour at Anfield chiefly due to a lack of an alternative.
Carvalho is a quality enforcer who would cost in the region of £20m and would no doubt jump at the chance of a move to the Premier League.