The Baggies confirmed on Friday they have taken disciplinary action against Odemwingie following his attempts to push through a move to QPR on transfer deadline day.
The club also said the Nigerian striker is available for first-team selection again after issuing an apology over the incident.
Enrique believes Odemwingie could be given a hard time by both the home fans and players on Merseyside should he make his comeback.
He said: "I'm not the type of player who would wind him up. But there will be songs and he will get it from other players.
"They will try to make him angry.
"I'm not this type of player. But a lot of players will do it."
Enrique was publicly criticised by Liverpool manager Brendan Rodgers earlier in the campaign and admits the comments made him angry.
But the Spaniard feels he has done well to change Rodgers' opinion of him, adding: "Of course I was angry - he said things in the press.
"But it was OK because I had to train harder and improve to make sure I was not finished here.
"Saying it in the press is not good but the truth is it worked with me.
"This is a big opportunity for me and I was not going to let it go."
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