Pochettino has been linked with the United job as pressure continues to mount on Michael Carrick, whose future is reportedly under review following another disappointing period at Old Trafford.
The club are believed to have approached the former Tottenham and Chelsea manager, who is currently in charge of the United States national team, to discuss personal terms.
However, Lovren is not convinced that Pochettino would be the right appointment, despite knowing the Argentine well.
Speaking to Hajper, the former Croatia international suggested that United's wider problems could make the job difficult for any incoming manager.
"I know Mauricio Pochettino really well, and I know what he likes, but I don't see him at Man Utd," Lovren said.
"He's quite smart and knows what's going on around the club, and there is definitely a bigger issue than just changing the manager."
Lovren also defended Carrick to some extent, suggesting that the current United boss has qualities but is working in an environment where the foundations are not strong enough.
"Even with Michael Carrick, you feel there is something good in him, but there is a bigger issue. The foundations are not quite right," he added.
The former Liverpool defender believes United's decline has gone on for far too long for a club of their size and stature.
"There is a period where things can go wrong, but now it's getting out of hand for how many years Manchester United has not been at the top for such a big club.
"I believe they deserve and always need to be in the top four, but you don't see it."
United chief executive Omar Berrada and director of football Jason Wilcox are reportedly among those pushing for a change, with the club's hierarchy expected to discuss Carrick's position.
Pochettino has previously missed out on the United job in 2018 and 2022, when Ole Gunnar Solskjaer and Erik ten Hag were appointed instead.
Crystal Palace have parted company with manager Pierre Sage following a disappointing run of results that has left the club struggling in both domestic and European competition.
Lewis Koumas is determined to make the most of his opportunity at Liverpool after breaking into the first team under new head coach Andoni Iraola, insisting there is nowhere else he would rather be.
Michael Carrick's tenure as Manchester United head coach has come to an end, with the club confirming his departure on Thursday afternoon.
Thomas Tuchel has reaffirmed his commitment to England, insisting he has unfinished business with the national team and intends to remain in charge until at least Euro 2028.
