The same publication had earlier claimed Fulham faced a battle with Newcastle United for the 24-year-old, but they now believe the London club will get the deal done.
And this is the latest development of a largely positive summer for the Whites, who impressed as they reached the Championship play-offs last term.
Fulham's thrilling style stunned a number of the league's high-flyers and they have fought off alleged interest in a number of key men in the transfer market.
While Scott Malone headed to Huddersfield Town, Tom Cairney and Ryan Sessegnon have both signed new deals - although Chris Martin, who netted 10 times last season, has returned to Derby County after a loan spell.
But a move for Rolan would arguably see Fulham recruit an upgrade on Martin, with the player suited to a counter-attacking game and established at a higher level.
Rolan has hit double figures in all competitions in each of his last three campaigns with Bordeaux, also scoring twice in Uruguay's current World Cup qualification campaign.
Had Cairney and Sessegnon departed this summer, an exciting Fulham outfit could have been dismantled after just one impressive season - but Rolan's arrival, combined with those renewed contracts, should make for another explosive year.