Dutchman also insists Liverpool are "still rebuilding" but admits Manchester City are big rivals although he feels the champions' winning mentality will again prevail
The Dutchman also claimed that neither Arsenal or Liverpool currently have what it takes to remove the trophy from Old Trafford.
"We are not afraid of anyone at all," Meulensteen told the Daily Star.
"[Manchester] 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."
Despite the big spending of local rivals City, Meulensteen also maintained that his side's experience in competing for honours year in, year out would give them a decisive edge.
"City have made very good signings, but we have something they don't possess. We know what it takes to win trophies," he said.
The 47-year old, who has progressed from a youth coaching position to the first team via the reserves, lauded United's crushing 8-2 win over Arsenal but expressed sympathy for Gunners boss Arsene Wenger.
"Our win over Arsenal was something special," he said.
"Their squad has lost a lot of quality with [Cesc] Fabregas and [Samir] Nasri's departures. It's as though nothing is going right for Arsene Wenger right now."