Collins has been on the books of West Ham since 2012, but there has been speculation in recent weeks that he could leave the London outfit next month.
According to The Sunderland Echo, Sunderland are interested in signing the 32-year-old central defender.
Bilic has made it clear in The London Evening Standard that he does not plan to sell the Wales international in January.
“For me, ‘Ginge’ is a manager’s dream,” wrote the Croatian. “It has not been easy for him at times because he has been out of the team for some periods.
“But before, during and after every training session or match, he has been an important part of my squad — he has been so positive.
“Up until the injuries, there was a possibility that one of our offensive players could possibly go in January, possibly on loan, but not now.
“If anyone wants to leave, if they come knocking on my door, then perhaps we would consider it, but if that doesn’t happen then no one will be going.”
Collins has made just six appearances in the Premier League for West Ham so far this season, creating one chance in the process.
The former Aston Villa defender has a pass accuracy of 83%, has won 18 headers, two dribbles and seven tackles.
West Ham are eighth in the Premier League table at the moment with 24 points from 16 matches.
The London outfit are five points behind Manchester United, who are currently fourth in the standings and occupy the final Champions League spot.