However, the Dutchman has admitted that the decision could be taken out of his hands, and the bookmakers William Hill make Gullit odds-on to have left Newcastle by the end of the season.
Newcastle's 4-2 defeat at Southampton on Sunday, when they conceded all four goals after the interval, cast further doubt on the manager's position with his side rooted firmly to the foot of the Premiership table with no points from three outings, and his post-match comments left a question mark over his future after just under 12 months on Tyneside.
But Gullit has since vowed to turn things round at St James' Park. "I thought I might have lost the support of the board, the fans and the players, but they have been good enough to support me," he said. "I really believe in this team and if they all support me, which it appears they are, and give me the time, I honestly believe that I can make this team work.
"I want to stay at Newcastle. I want to take this club to where it has to go. I did not say I was going and I did not say I was leaving when I was asked if I would be here next week. But this is in the context that, if you are a manager and you are losing matches, you can be sacked. I do not want to go from Newcastle United of my own accord."
In a somewhat strange aside that begged more questions than it answered, Phil Smith, Gullit's agent, said yesterday morning on Radio 5 Live: "Maybe an inspirational performance or two from the captain [Alan Shearer] would help."
The club insisted yesterday that nothing has changed. "It's business as usual," said a spokesman. "There will be no press conferences and no statements."
Wimbledon are the visitors to St James' Park on Saturday and Egil Olsen's team are sure to provide a physical contest. Newcastle must match them without captain Shearer, who is serving out the one-match ban for his sending-off against Aston Villa on the opening day of the season.
Whatever happens against the Dons, Gullit's immediate future could be decided four days later, at least in the eyes of the fans, when United entertain arch-rivals Sunderland on 25 August.
Shearer is certain Newcastle can shrug off their woeful Premiership start and enjoy a successful season. He backed the United squad to improve and refused to comment on the position of Gullit.
Sunday's embarrassing defeat by Southampton was Newcastle's third successive loss following Gullit's summer spending spree but Shearer said: "Before the season started we all felt we could win our first three games - and that has not happened. We've got to pull together and we can get through this.
"We believed we could be successful. Whether we can still be successful remains to be seen, but I believe we can. I hope we can just turn the corner and push as far as we can.
"We are all very disappointed with the way the season has started. We've got to keep plugging away until we get some points or a win, and hopefully that will take us on to better things."
Gullit was reported to have been close to resignation after the Southampton defeat, but Shearer said the club had asked all players to remain silent on the issue.
The England striker, who opened his account for the season with a penalty against Southampton, shrugged off personal criticism about his own form.
"I am up there to be shot at. I have to take criticism as well as praise," he said. "As long as I can look at myself in the mirror when I come off the pitch and know I've done my best, I am happy."
Geordie Shearer is widely tipped to manage his home-town club in the future. His new improved contract, which ties him to Newcastle until 2004, is thought to contain a clause which gives him the chance to manage the Magpies, but he remained tight-lipped on the subject as he helped launch the AXA FA Cup Road Show in central London yesterday afternoon.
Newcastle have been hit hard by injuries and suspensions which have hindered progress at the start of the new season. More than pounds 15m of talent was unavailable to Gullit at The Dell.
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