Harry Maguire, who could face United for Leicester today, Bayern Munich's Jerome Boateng and Toby Alderweireld of Tottenham Hotspur were all linked with United, while Atletico Madrid's Diego Godin emerged as a late target yesterday.
But RMC says Pogba has now put talk of a move to bed by vowing to stick around in Manchester until the end of the current campaign.
It lead the Portuguese to vent his feelings after the final whistle at Old Trafford and reiterate his warning for the new season.
"It's important to win and play well, we played well in periods against a good team that invest more than us".
The season opener will start at 8 pm local time, 12:30 am IST (Saturday) and 7 pm GMT.
Leicester looked startled by United's early intensity but began to fell their way into the match as debutant James Maddison impressed and their wide men made in-roads.
"I can't remember the last time I had a break and a long vacation", he told United Review ahead of Friday evening's clash against Leicester City.
José Mourinho does not expect any Manchester United deadline-day signings
The Premier League is back this weekend - and we travel to Arsenal to begin the defence of our title. The manager has to decide which way we play.
There has been speculation that Pogba wants to leave the English giants because he and manager Jose Mourinho do not see eye to eye on a number of things.
But for all that could have been this summer, Mourinho certainly has the talent at his disposal to make this a successful season, especially if Pogba can replicate Friday night's display.
"The players from a year ago are responsible for the excitement, and then we brought in a few new players as an icing on the cake", Klopp said during the club's promising preseason tour in the United States.
He went on to repeat his sentiments that United are in for a tough season, after they overcame opponents who spent more cash in the summer transfer market.
Mourinho also confirmed Pogba had his blessing to take the penalty after what appeared to be a disagreement with Alexis Sanchez.
He didn't give United enough of a threat against a very weak looking Leicester right-hand side and when he did get the ball, he was often wasteful and sloppy making the wrong decision more often than not. I needed more changes, but I couldn't so it was not easy to manage the game from the touchline point of view.