Ramsey is in the final year of his Arsenal contract, and the Gunners are "desperate to tie him down" to a new deal, per the report.
The 27-year-old is one of Arsenal's most important players, but his contract situation will be cause for concern. If he does not sign an extension, he will be able to walk away for free next summer.
The midfielder is widely regarded as a complete player. He is strong in the tackle, can win back possession, is great in possession and has an eye for goal.
He has also provided some memorable moments since joining from Cardiff City in 2008. He scored the winning goals for Arsenal in both the 2014 and 2017 FA Cup finals.
Ramsey is well aware of his importance to Arsenal and will want his new contract to reflect his standing at the club.
Mesut Ozil is Arsenal's highest earner after he signed a new contract worth £350,000 per week earlier this year, per Jeremy Wilson at the Telegraph.
There has been speculation Ramsey wants £300,000 a week to stay at Arsenal. However, his representatives, Avid Sports, have denied such reports, as shown by James Benge at the Evening Standard:
Manager Unai Emery has spoken about the midfielder's future and said "it's very important he says with us," per Danny Wittenberg at the Mirror.
Emery will hope to resolve Ramsey's contract situation quickly to avoid the drawn-out saga that happened last season with Ozil and Alexis Sanchez.
And as Benge noted, addressing Ramsey's standing will be the club's No. 1 priority:
Ramsey may be waiting to see how the season unfolds under new manager Emery. The Spaniard replaced Arsene Wenger after 22 years in charge of the club. It's a new era for the Gunners, which makes them something of an unknown quantity.