Grant is determined to keep hold of Parker and insists the former Chelsea and Charlton star is key to West Ham's long-term plans.
"Yes, he is staying at the club," Grant told Sky Sports News. "He is a good player and it doesn't surprise me that many good teams would want him as he could play for any team in the Premier League.
"But we have plans for next season, not for one season for all the team. We have a vision about the club to have West Ham in a good place and good football and he is a big important part for this project."
Asked if he feared Spurs might make a new bid for Parker, Grant said: "I think they don't have to make a bid because we make it very, very clear that Scott Parker will stay with us."