The Manchester United midfielder is out of contract at the end of the season and is set to leave the club.
United’s executive vice-chairman, Ed Woodward, chose to activate a year-long extension on Herrera’s contract last summer instead of negotiating a new deal.
It had previously been reported that Paris Saint-Germain were set to sign the 29-year-old.
According to French publication, L’Equipe, Arsenal could make a late move for Herrera as Unai Emery is a big fan of the midfielder.
Herrera’s protracted signing from Athletic Bilbao was completed in 2014 when United met his £28.85million buyout clause.
He has gone on to make 187 appearances for the club and won the FA Cup, League Cup and Europa League.