Enrique, who entered the final 18 months of his current contract at the turn of the year, has been attracting the attention of Manchester City and Liverpool in recent weeks, with Saturday's scintillating performance against Blackburn providing another graphic illustration of his strengths.
There is every likelihood of a bid being lodged this summer, and in an ideal world, Magpies manager Alan Pardew would like to ward off any attention by agreeing a new deal with the Spaniard.
However, while Joey Barton has expressed a willingness to conclude contract talks shortly, Enrique has consistently refused to discuss a new deal until Newcastle's Premier League status is secure. As a result, an agreement is unlikely to be reached until the end of the season.
Jose's situation is simple, said Pardew. He's made it clear that he won't talk to us until we're safe. What are we now, 32 points Well we're not safe are we So that makes the situation clear, and to be honest, it makes a lot of sense for both him and us.
He is an outstanding player and we know that. He is an important player for this team because a lot of our play goes through him. He is involved in a lot of the good stuff that we do and I thought he was superb (against Blackburn). In terms of technique and impact, I thought he was the best player on the pitch by some distance.
Enrique is certainly a different player to the hesitant left-back that rarely looked comfortable as Newcastle tumbled out of the top-flight two seasons ago.
A spell in the Championship has clearly given him the confidence to express himself going forward, and his relationship with left winger Jonas Gutierrez is a key facet of United's attacking play.
His delivery on the run is superb one cross in particular at the weekend, which Peter Lovenkrands failed to reach at the near post, took the breath away and Pardew has openly encouraged the 25-year-old to push forward positively whenever possible.
I'm just trying to put my mark on the team, he said. I've always played a team which is on the front foot and encouraging full-backs to push on. Enrique's performance exemplified that, and if anybody deserved to win a game it was him because he was magnificent.
I'm just very pleased with the reaction I've had from the staff and the players in terms of what I want to achieve. My style is perhaps a bit different to Chris' (Hughton) and the way we controlled this game was pleasing to see.