no the rules just say (since 2022 apparently)
Clubs may not register more than two players on loan at any one time from other Premier Legaue clubs.
The maximum number of loans registrable in the same season is four, and, under no circumstances, shall more than one be from the same club at any one time.
Premier League clubs cannot loan to another Premier League club a player they have acquired in the same transfer window.
A Premier League club may loan not more than one of its goalkeepers to another Premier League club.
thats literally all the rules on loans.