4:48 PM PT -- A rep for Ajayi tells TMZ Sports the lawsuit is bogus ... adamantly denying Jay ever physically pushed the owner of the home.

They also deny Jay damaged the property in any way ... or hosted any parties.

Instead they claim the owner tried to get Jay and his friend to pay him cash directly -- bypassing the Airbnb website -- so they say they left the house several days early ... but still paid the full rate.

Ajayi's people also say the group filed a complaint against the home owner with Airbnb.

NFL star Jay Ajayi shoved the owner of a fancy L.A. mansion who charged the Eagles running back $25k in damages for trashing the place ... this according to a new lawsuit obtained by TMZ Sports.

The 24-year-old is being sued by the owner of a swanky 6,000 square foot pad located above the famous Sunset Strip ... where the RB and a friend stayed back in February for 5 days after Ajayi won the Super Bowl.

According to the suit, Ajayi and his buddy threw at least 3 parties at the house despite the fact they were specifically told -- NO PARTIES!

In fact, the owner claims he charged a $5,000 fee for each party at the home ... which Ajayi never paid.

Additionally, the owner claims Ajayi broke a table, scratched some floors and violated the no smoking rule.

In total, Ajayi racked up $25,000 in penalty fees -- but when the owner confronted Jay on Feb. 18, he claims Ajayi "pushed [him] on [his] chest in a menacing and threatening manner."

The owner describes the incident as battery -- and said he had to call local security to remove the NFL star from the property.