Payet has emerged as one of the league's leading midfielders since joining West Ham from Marseille in the summer, scoring six goals and providing four assists in 18 appearances.
The France international's exploits have helped West Ham up to sixth position in the Premier League and while he signed a five-year deal upon his arrival at Upton Park, Bilic is ready to offer the 28-year-old improved terms.
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Bilic said: "We are moving, the club is moving, with the new stadium, with the revenue and everything. We have to move and the most important move is to keep your best players and to add some new players who are needed and Dimitri Payet is our best player – I have no problem whatsoever to say that.
"Of course, I would love to have him happy, long term, at the club.
"He signed only a few months ago but he has made a huge impact – a very, very huge impact – and while he has a long contract, five-and-a-half years, he is in a good position.
"It is not only the staff and the players but also the fans and the board, we all want to keep him for a long, long time."