The 24-year-old was a regular for the Red Devils during the 2020-21 campaign, making 40 appearances in all competitions, but he struggled for action in the latter stages of the season.
Pereira has not been involved in any first-team match for United this term, having seemingly been deemed surplus to requirements by head coach Ole Gunnar Solskjaer.
According to Il Messaggero, Lazio are closing in on a deal for the Brazil international, who is expected to join the Serie A outfit on loan for the 2020-21 campaign.
The report, though, claims that the Italian side would be obliged to sign Pereira on a permanent deal next summer for a figure in the region of €10m (£9.1m).
The South American has scored four times and registered five assists in 75 outings for United.