France midfielder Matuidi, 26, is out of contract at the end of the season and scored in PSG's 3-1 Coupe de France victory at the Stade Jacques Chaban-Delmas.
Matuidi emerged as a substitute for the Ligue 1 champions, who might also have to fend off interest in highly-rated Italian international Marco Verratti, linked with a summer transfer to Real Madrid.
Moyes was in attendance for Juventus' 4-1 win at Cagliari on Sunday, where he watched defender Davide Astori, Claudio Marchisio, Paul Pogba and Arturo Vidal.
Pogba, however, is a major target for PSG, and any move would offset the loss of Matuidi, should he leave at the end of the season.
Renowned for his fastidious scouting at Everton, Moyes is eager to address United's central midfield malaise which has harmed their prowess in the Champions League since their 2008 win.
He has watched Atlético Madrid's Koke already this season and United coach Phil Neville flew to Spain over the weekend to monitor Atléti's Saúl Ñíguez, on loan at Rayo Vallecano.
Marouane Fellaini, still out injured, was the club's first central midfield signing in six years when he joined from Everton on deadline day in September.