Ramsey has been locked in contract discussions for the past few months with his current deal running out at the end of the season.
The Welshman had been ready to stay and Arsenal were confident of keeping hold of him.
It’s believed that Arsenal turned down a £50million bid for Ramsey last summer, with Manchester United, Chelsea and Juventus among those keen to sign the 27-year-old.
Ramsey feels he deserves an increased salary due to his status as one of Arsenal’s most important players.
However the Mirror now claim that no new contract deal will be offered and that Ramsey will leave on a free next summer.
Ramsey scored the winner in two of Arsenal’s three recent FA Cup final victories and has been a regular in Unai Emery’s squad this season.
Former Arsenal defender Nigel Winterburn believes Ramsey is key to Arsenal and would fit in at either Chelsea or Manchester United.
“With less than a year remaining on his contract, Ramsey is in a very strong negotiating position and is also a very attractive proposition for a lot of big clubs around Europe,” Winterburn said.
“I’m sure lots of top clubs are monitoring the situation and are ready to poach him.
“I think Manchester United and Chelsea will both battle it out to sign him if they feel he is seriously considering leaving Arsenal.
“I don’t think he could get into the Manchester City and Liverpool teams, but it would hurt Arsenal fans to see another of their superstars leave to a Premier League rival.
“I hope Ramsey signs a new contract at Arsenal.”
Discussing Ramsey’s future during the summer, Emery said: “The contract is one thing for the club and the player.
Football changes every day. I think about the match today first, then training tomorrow, the match on Saturday and to continue our preparation.
“I think Aaron is an important player for us. For me, I want him to stay with us, to work with us, to give the team the big performances with his quality.”