The 26-year-old has netted 28 times for Brendan Rodgers's side in all competitions this season, staking his claim for the award come the end of the season.
Enrique told the club's official website: "Van Persie and Bale are on fire. Van Persie has been a very important player for Manchester United this season and Bale is doing very well - in the last few games, Spurs have won because of Bale's goals.
"It will be difficult for him but, of course, I think he deserves it. But Luis is my friend, so I would like him to win the Player of the Year award."
Liverpool face Tottenham Hotspur in the Premier League this Sunday.