Ramsey's future continues to fill column inches after the Gunners withdrew a contract offer for the midfielder, triggering a host of interest from a number of outfits.
The Reds were expected to be one of the Premier League clubs that desire Ramsey, but Liverpool manager Jurgen Klopp has notified Arsenal he will not be in the mix to capture the player.
According to Dawson, Ramsey is prepared to consider a switch to one of Arsenal's rivals, with Manchester United and Chelsea reportedly interested if he departs the Emirates Stadium on a free transfer.
Per Sky Sports Premier League, Ramsey said he will continue to do his best for the Gunners until his future is resolved at the end of the campaign:
Despite Ramsey stating his intentions, Arsenal manager Unai Emery could still try to sell the player to generate a small transfer fee in January, but it appears the midfielder will resist such a move.
Ramsey has been a loyal servant to the Gunners, but Emery is building a new side with fresh faces and new tactics.
The Welshman will be in demand because of his wealth of Premier League and European experience, and he will land at a top club in the summer.
Scott Paterson of the Mirror wrote Ramsey would be a good capture for United boss Jose Mourinho, but he's not the top-class player supporters at Old Trafford really want.
"The Welshman is a decent player and on a free transfer, or potentially a discounted fee in January, United could certainly do worse. He will bring the added experience and composure that United are often lacking.
"But if their aspirations are to close the gap between them and City, he’s hardly the marquee signings the fans would crave."
Klopp clearly does not need Ramsey. His midfield is fuelled by a number of diverse talents, and the Welshman would struggle to get in the starting XI.
Former Gunner Alex Oxlade-Chamberlain will add further depth to the Reds midfield when he returns from injury, with Klopp relying on players with stamina at his core.
Ramsey remains a fine professional, and it's a surprise Arsenal withdrew a pre-existing contract offer.
However, with the winter and summer transfer windows ahead, Emery will have plenty of time to bring in a central midfielder who fully suits his selection as Ramsey departs.