Liverpool are said to be the leading English team in the race to sign Manolas, with the Reds willing to triple his wages to lure him to Anfield.
But the Greece international may not even leave Italy this summer if Inter get their way.
According to Italian newspaper Gazzetta dello Sport, Roma chairman James Pallotta wants £35m paid over three instalments for Manolas.
However, Inter are hoping to undercut that price by throwing in defender Jeison Murillo as part of a cash-plus-player deal.
Murillo is out of favour with Inter manager Stephano Pioli and is tipped to leave the San Siro club in the summer.
Inter are believed to be pushing for an agreement months before the summer transfer window opens, knowing that financially they may struggle to fend off Premier League clubs.
Liverpool had scouts at Roma’s Europa League clash with Lyon last Thursday, while Manchester United employees are also said to have tracked him over this season.
Manolas signed a five-year, £25,000-a-week contract at Roma in 2014, with Liverpool prepared to offer him a £75,000-a-week deal.
Arsenal are said to have turned down a £35m offer to sign Manolas last summer, which was supposedly down to his former club Olympiakos earning a 50 per cent cut in the deal.