But the Toffees could face competition from Manchester City, who will reportedly move for the Greece international if they fail to land Stones.
The report states that Manolas is valued at £20 million by Roma, but later suggests that a bid close to £12 million - the price they paid Olympiakos two summer ago - could tempt the Italian giants into selling.
For a 24-year-old international with three years to run on his contract, £12 million seems like a fair price.
However, not when they could have had him for twenty-four times less in 2012.
According to BBC Sport, Everton agreed a £500,000 fee for Manolas, then with AEK Athens, but were forced to put the deal on hold while they concluded the transfer of Nikica Jelavic from Rangers.
And the Toffees could miss out again even if Stones does leave, with the report linking Arsenal and Chelsea as potential suitors.
According to the Mirror, the Gunners saw a bid of £5.5 million plus add-ons knocked back last year.