Ramsey has less than a year remaining on his contract at the Emirates Stadium, and it was claimed on Thursday that Arsenal have withdrawn their contract offer to the Wales international.
The 27-year-old would be able to leave the Gunners on a free transfer at the end of the campaign should the situation remain the same, but according to The Mirror, the Premier League side are open to doing business midway through the season.
Arsenal acted in a similar manner when allowing Alexis Sanchez to join Manchester United at the start of 2018, and the club's hierarchy do not want to lose one of their star men for nothing.
However, Ramsey could potentially decide to remain with Arsenal until the end of the season in order to give himself a wide range of choices for his next move in the summer.
Teams from England and Europe are likely to show an interest in the playmaker, who has been with Arsenal since 2008.