Israeli boss hopeful of completing a deal for Steve Sidwell
Recent reports pointed towards Aston Villa midfielder Steve Sidwell holding advanced discussions with the Hammers, before taking a medical at the east London outfit.
And with the former Chelsea midfielder expected to join the relegation threatened club in January, it had been thought that Parker could be sold.
However, the Israeli boss insists otherwise, as he told reporters: "No chance.
"Scott Parker is more than a good player for this football club. Even though we are at the bottom, we are trying to do the right things for this club.
"We know all the teams that succeeded did not have it so easy at the start.
"He is one of the foundations of this club. The owners have made it very clear that they want Scott Parker here and want good players here.
"We don't have many like Scott Parker and it would not be good for us if he left the club and I don't think it would be good for him. He knows what the vision of the club is and he is part of it."
The former Chelsea boss also confirmed that the club are looking to tie up a deal for Sidwell, and said: "Normally I don't speak about players when we didn't complete the signing but I am interested in him.
"He is a good player and a good lad. We are trying to build a team here with positive guys and intelligent players and he is very intelligent and I hope we will complete the deal. He has done what he needs to do to be here."
Manchester City defender Wayne Bridge and winger Shaun Wright-Phillips, and Tottenham Hotspur forward Robbie Keane and Jonathan Woodgate have all been linked with a move to Upton Park.
But Grant refrained from confirming the club's potential transfer targets, as he added: "It is not a secret that we have a lot of injuries and that we need to make the squad stronger and that is what we will try to do in January.
"A lot of players have been linked with us."
West Ham now have a Boxing Day clash against Fulham, who have only one victory in their last 14 games in all competitions. At the moment, the Cottagers are outside the dreaded drop zone only by virtue of a superior goal difference over 18th placed Wigan Athletic.
The Hammers, however, remain at the rock bottom of the Premier League.
"We want to play like we did last week when we were better than Blackburn [which ended in a 1-1 draw] and we want to take points because we need them," said Grant.
"I think [Fulham manager] Mark Hughes is under pressure, but Wolves are under pressure, Wigan are under pressure, Blackburn are under pressure and at the top the six teams are under pressure.
"This is the name of the game. We are under pressure to take points because we are at the bottom.
"We don't deserve to be at the bottom, having analysed our games, but there are no points awarded for 'deserve'."
The general perception is that a team that is at the bottom of the table during Christmas is one that will be flushed down into the Championship come May, since West Bromwich Albion in 2005 remain the only side to have ducked that trend.
But the manager remains positive in his outlook, insisting that his side can avoid relegation.
The former Portsmouth manager said: "For me, what has happened in the past is good and tradition is good but things happen that didn't happen in the past.
"Nobody thought a guy could run a mile in under four minutes because nobody had done it before, so there are a lot of things that nobody has done before but we want to do it and we can do it."