This is according to The Sun, who claim scouts from the Camp Nou club will also run the rule over the 24-year-old at next weekend’s FA Cup final between the Gunners and Aston Villa at Wembley Stadium.
Barcelona head coach Luis Enrique reportedly sees Ramsey as the perfect acquisition for his “energetic passing game” alongside Andres Iniesta and Sergio Busquets.
The recently-crowned La Liga champions can still sign players this summer, despite their transfer ban, but are prohibited from registering them until January 2016.
This means Barcelona could potentially sign a pre-agreement with Arsenal and then wait until the New Year before playing the Welsh midfielder - provided they can strike a deal with the Gunners - or secure his services and then loan him out elsewhere for the first half of the 2015-16 campaign.
Arsenal will be desperate to keep Ramsey
But Arsene Wenger is expected to do everything in his power to keep Ramsey, who was magnificent last season, at the Emirates Stadium.
A much-maligned figure in the past, the former Cardiff City starlet has flourished over the past 24 months and developed into one of the Premier League’s most consistent central midfielders.
It’s unlikely that a bid even in excess of £50 million will tempt Wenger into selling one of his best performers, particularly with the club seeking to end their 12-year wait for a league title next season.
Barcelona's interest is a surprise
That Barcelona are reportedly keen on Ramsey is slightly surprising for a couple of reasons.
First of all, where would the signing of Ramsey leave Ivan Rakitic, who has been fantastic since his arrival from Sevilla last summer.
Secondly, reports in Spain on Thursday claimed Borussia Dortmund midfielder Ilkay Gundogan had passed a medical with Barcelona, and there is no chance of the Catalan giants spending mega money on two new central midfielders - who play in identical positions - during the forthcoming transfer window.
Furthermore, it’s also understood Barcelona are leading the race to sign Juventus midfielder Paul Pogba, whose preference is to join the Champions League finalists this summer.
But, in terms of quality, Ramsey would certainly be a useful addition to Barcelona’s squad - and the opportunity to work with the likes of Lionel Messi, Neymar and Luis Suarez would surely appeal to any player with the hunger and ambition to reach the very top of their profession.
Arsenal fans: should Arsene Wenger sell Aaron Ramsey if Barcelona offer over £50 million? Have your say in the comments below!