Sir Alex Ferguson's assistant also believes local rivals Manchester City, tipped as serious contenders for title success this term, will not be able to compete with United's experience in winning silverware.
The Red Devils, targeting a 20th championship this season, are currently top of the table after securing wins in all three of their opening games, including their emphatic 8-2 rout of Arsenal last weekend.
And Meulensteen claims United have nothing to fear from any of their top-four competition, insisting the Gunners have regressed and Liverpool are still rebuilding.
He told the Daily Star: "We are not afraid of anyone at all.
"City have made very good signings, but we have something they don't possess. We know what it takes to win trophies.
"City are still a big rival. But Arsenal have gone backwards, Liverpool are still in a stage of rebuilding and Chelsea have just made one major signing in Juan Mata.
"Besides, Chelsea's squad is too old, and their tempo is not high enough to win the Premier League."
Meulensteen believes the threat Arsenal posed has been diluted by the exits of captain Cesc Fabregas and key midfielder Samir Nasri this summer.
"Our win over Arsenal was something special," he added.
"Their squad has lost a lot of quality with Fabregas and Nasri's departures. It's as though nothing is going right for Arsene Wenger right now."