The 27-year-old Espanyol ace shone for his nation at the World Cup last summer, earning praise for his showings in Brazil.
He damaged his knee at the tournament, but that has not deterred the north London duo, who have been monitoring his recovery and progress.
Reports suggest that Moreno may be available for as little as £5m in a few months’ time, which puts him firmly in the ‘gettable’ zone for the rivals.
Both clubs are believed to be looking at making defensive additions.
The enforcer has been limited to just 12 La Liga appearances this term due to the aforementioned knee issues, but is still considered to be one of the division’s better defenders away from the elite teams.