Liverpool have already spent in excess of £100m this window but McGarry has stated that the Reds are interested in signing the Welshman before the season starts.
Speaking to the transfer window podcast, as quoted by the Daily Express, McGarry said: "There’s a little bit of interest from Liverpool, I understand.
"I think there’s no vacancy at Liverpool right now following the arrival of Fabinho and Naby Keita but Ramsey would certainly be a very good addition to Jurgen Klopp’s squad as a creative box-to-box midfielder. So, Ramsey is taking time and quite rightly to weigh up his options."
The former broadcaster also suggested that Ramsey may follow in the footsteps of his compatriot Gareth Bale and look to play his football outside of England when his contract ends.
"I don’t think he’s particularly worried about moving (by the deadline) because as of January he can sign a pre-contract with any club outside of England as Emre Can did with Juventus and move next summer for free when the fee that would be demanded for him now - £35m to £40m - would be paid to him in wages as a signing on fee."
McGarry continued: “To me, Ramsey is again one of the few candidates of British players who would happily go abroad and ply his trade and learn the language and fit in and be a success. So his options are not purely limited to the Premier League."
When quizzed about the midfielder's future, after Ramsey missed the pre-season fixture against Chelsea, Arsenal boss Unai Emery stated: "Ramsey's with us. The contract is a question for the club and for the player. My opinion is clear, I want him to be with us."
The Spaniard added: "He's the type of player I want in this team. But the contract is one thing only for the club and the player."