Arsenal were beaten 1-0 by Everton at Goodison Park on Sunday afternoon, with the Gunners missing out on the chance to take another step towards the Premier League top four.
Phil Jagielka scored the only goal of the game and produced a solid display as the Toffees claimed another major scalp.
But, while Arsenal were admittedly far from their best, Gueye was the standout performer from both sides.
And, with Manchester United primed to lose Ander Herrera, they could do a lot worse than going after the Senegal international.
This summer, Herrera looks destined to jump ship to PSG.
United are refusing to bow to his wage demands with the Spain international asking for a substantial pay rise.
And the departure of the former Athletic Bilbao star will leave a sizeable hole in Ole Gunnar Solskjaer’s midfield.
Gueye, however, would be a brilliant replacement.
So far, United have been backed to move for the likes of Bruno Fernandes and Tanguy Ndombele, of Sporting Lisbon and Lyon respectively.
But Gueye would be a safer bet.
The 29-year-old has been attracting interest from Ligue 1 giants PSG, who would like to make him their own replacement for Lassana Diarra.
Yet, for United, he would represent a safe signing.
Against Arsenal on Sunday he pulled the strings in the middle of the park with a performance full of enterprise, dynamism and tenacity.
How the Red Devils could do with that next season.
The Everton star will likely leave in the summer and the Toffees, as shown with the sale of Romelu Lukaku, are not opposed to doing business with United.
Gueye could be United’s version of N’Golo Kante.
And his performance for Everton against Arsenal suggests he would be the ideal way to coax more consistency from Paul Pogba.