Pochettino has been on the radar at Old Trafford for some time, with Sir Alex Ferguson a big fan of the Argentine coach.
The former Tottenham manager remains in place at PSG for the time being, but he is interested in taking the United job in the summer, according to the Daily Mail.
Should that eventuality come to pass then he is sure to have a say on transfer activity at Old Trafford over the summer.
One name he could put forward is Gallagher, who has impressed hugely on loan with Crystal Palace from Chelsea this season.
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It seems more likely, therefore, that Gallagher’s long-term future will be decided once the 2021/22 season has reached its conclusion.
Chelsea could fight tooth and nail to keep hold of their academy graduate, with Tuchel impressed with what he’s seen from the midfielder.
“I am not surprised the national coach loves him because I loved him from day one,” Tuchel said in November.
“Humble, nice, smile on his face and all the time ready to give everything, want to learn and improve.”
He added: “As a team-mate I would have loved to play with him. It is a pleasure to know him; I am super happy that it has worked out so well. He needs to keep his feet on the ground.”
Yet keeping him at Stamford Bridge could prove difficult, especially if Pochettino finally makes the long-touted move to United.
After splashing the cash to bring in Jadon Sancho, Raphael Varane and Cristiano Ronaldo in the summer, United are targeting a central midfielder in 2022.
United lack depth in the middle of the park and Gallagher could be a good addition to a squad that currently relies on Scott McTominay and Fred in the position.