However, the significant progress they thought they had made was knocked back by the Merseysiders who countered claims a £75m (€85.1m) fee had been agreed by insisting no deal has been struck.
And that has left Chelsea, who appeared front-runners in the race to re-sign their former player, with an opening to still make a late intervention.
Everton will hope that is the case as it increases the chances of a bidding war to take the asking price closer to the £100m (€113m) tag they privately put on the 24-year-old Belgium international.
However, they may have to accept less for a player who has regularly voiced his desire to play in the Champions League.
But with the Stamford Bridge club yet to show their hand United remain in the driving seat to secure a player understood to be Jose Mourinho’s first choice and one they have been quietly pursuing for months while all the talk was of an impending move to Chelsea. It is understood United believe they have secured their primary target, and a reunion with Mourinho for Lukaku, but senior sources at Everton maintain no deal or agreement over a fee has been reached.
United are believed to have ended their interest in Real Madrid striker Alvaro Morata after making progress with Lukaku, with the club hoping to get a deal over the line before heading to the United States on their pre-season tour.
United captain Wayne Rooney looks increasingly unlikely to be on the plane this Sunday, with a return to boyhood club Everton getting closer — a move that is not understood to be connected to the Lukaku deal.
With Zlatan Ibrahimovic having already left Old Trafford this summer however, the signing of Lukaku would presumably ease the way for Rooney to leave.
The 31-year-old’s future has been the subject of considerable speculation in recent months, with reports linking him with moves to the United States and China.
But a return to boyhood club Everton has always seemed a strong possibility too, and it would appear that does appeal hugely to the former England captain.
Rooney left Everton at the age of 18 in a £30m (€34m) deal in 2004. He has since been one of United’s most influential players and overtook Bobby Charlton to become the club’s record goalscorer last season.
He has also won five Premier League titles and the Champions League during his time at Old Trafford.
But aside from breaking Charlton’s record in January - and if he leaves he would do so with 253 United goals to his name — last season was a frustrating one.
Rooney was unable to command a regular starting place in Mourinho’s side and started just 15 Premier League games.
He is contracted until 2019 but it has been reported a deal could be reached allowing him to return to Everton, where he first burst onto the scene as a 16-year-old, on a free transfer.
His signing would also continue a busy summer of transfer activity at Everton.
The club have already spent over £90m (€102m) on Michael Keane, Davy Klaassen, Sandro Ramirez, Jordan Pickford, Henry Onyekuru and Nathangelo Markelo have already been completed with Olivier Giroud and Gylfi Sigurdsson also linked.