The two Premier League giants - along with leaders Liverpool - have been credited with an interest in the Spartak Moscow midfielder, but it appears as if he has his eyes set on a possible move to La Liga.
"They are only rumours, nobody has told me anything. But I am very happy to be linked with the club," he told Sport of Barcelona's apparent interest in an interview that was cited by talkSPORT.
"They are a very big team, and all players want to play there. Of course I would like to play at Barca – who would not like to?”
23-year-old Borges - a senior Brazilian international - joined his current club from Campeonato Brasileiro Série B outfit Vasco da Gama in 2012 and has evidently impressed at Lokomotiv Stadium.
However, while he looks to be keen on a move to Barcelona, it remains unclear whether such a move - at least in the near future, anyway - will be possible with the club having recently been handed a two-window transfer ban after allegedly breaking rules over international transfers of U18 players.
While Borges' views on the Premier League are unclear, it could be that a move to one of the three English clubs that appear to be pursuing his signature could be more realistic.
Chelsea - who brought combative Serbian Nemanja Matic back to Stamford Bridge back in January - could have a need for a new midfielder in the summer, particularly with doubts appearing to surround the future of John Obi Mikel and possibly even Frank Lampard.
Arsenal boss Arsene Wenger - who has seen his team endure another late-season collapse in their forlorn pursuit of silverware - must be on the lookout for several high-quality new recruits this summer, while Liverpool will surely have to increase their strength-in-depth if they are to successfully compete on a level playing field in the Champions League next year.