This is according to Barcelona-based newspaper Sport, who understand the pre-candidate in question is hoping to take advantage of the poor relationship that currently exists between Ramos and Real Madrid president Florentino Perez.
Ramos, who is also on the radar of Manchester United, Manchester City and Chelsea, wants an improved contract from Real Madrid - the report suggests the 29-year-old wants to earn almost double what he currently does - and has voiced his concerns about Perez's controversial decision to sack the popular Carlo Ancelotti.
Because of his contractual situation, Ramos is unlikely to come out and publicly deny these reports linking him with a shock move to the Camp Nou. His representatives, meanwhile, will be acutely aware that interest from a potential Barcelona president will put significant pressure on Real Madrid to hand the World Cup winner the terms he feels he deserves.
Real Madrid simply cannot allow one of their key players to leave the Bernabeu for Barcelona - although the odds of Ramos actually accepting a formal offer are, as Sport correctly state, "practically impossible".
Could Ramos become the new Luis Figo?
But people might have said the same about the Portuguese winger Luis Figo 15 years ago.
Figo is one of the few top players to have moved directly between Barcelona and Real Madrid - but the horrible scenes from the 2002 Clasico, which famously included the head of a dead pig being thrown on to the Camp Nou pitch, serve as a stark warning to any player hoping to make a similar move in the future.
Real Madrid must keep Sergio Ramos
Ramos, 29, is very unlikely to join Barcelona but the mere fact a presidential candidate at the Camp Nou feels a potential deal with the vastly-experienced defender is not beyond the realms of possibility is somewhat significant.
The Spaniard, who has made over 400 appearances for Real Madrid and 128 for La Roja, is a hugely important player to Real Madrid.
Not only is he one of the best defenders in Europe, but he's also a huge threat from set-pieces at the opposite end of the pitch. Ramos has scored a magnificent 55 goals for Real Madrid since arriving from Sevilla in the summer of 2005.
Amongst that tally was one of the most important goals in Real Madrid's history: the last-gasp equaliser against Atletico Madrid in the 2014 Champions League final, which eventually allowed Los Blancos to finally secure the tenth European Cup that had eluded them for so long.
Is there any chance of Sergio Ramos swapping Real Madrid for FC Barcelona? Have your say in the comments below!