TalkSPORT says United are again watching Suzuki this season.
The Japan international left Sint-Truidense for Parma last summer.
The 22-year-old has played 19 matches in Serie A and kept a clean sheet three times.
Suzuki was close to joining United as early as the summer of 2023, but did not want to be a backup to André Onana and chose Sint-Truidense.
His contract runs until the summer of 2029. Parma hopes to keep him for at least one more season.