The 23-year-old midfielder joined team-mate Ali Crawford in penning a new three-and-half-year deal with the Scottish Premiership’s surprise leaders on Friday morning.
The contracts will keep the pair at New Douglas Park until May 2018 and out of reach from interested clubs for the time being.
But Gillespie had to backtrack after telling Sky Sports News he was “hoping to get a move” at the end of the season.
He said: “I’m in no hurry to move. I said on TV that I was looking for a move but that was a slip of the tongue.
“My mind went blank and I didn’t know what to say. What came out I instantly regretted. I’m delighted to be here for the next three years.”
Around 30 scouts from English clubs were in Lanarkshire last Friday to see Alex Neil’s shock troops beat Aberdeen 3-0 and would have been impressed by the displays of Gillespie and Crawford, who were both out of contract.
Accies, though, have acted swiftly to ensure they don’t lose out on the same kind of seven-figure windfalls which the sale of former stars James McCarthy and James McArthur netted the club.
But Gillespie - who joined Hamilton at the age of 15 - has not completely ruled out following the same path as the Everton and Crystal Palace midfielders.
“If I can do half as much as the two James’ have done in football I would be happy,” he said. “They are role models for everybody at this club, whether you are in the under-10s or the first team.
“I look up to those two and hope to emulate them.”
Crawford, also 23, knows he will have to fulfil the early promise he has shown for Neil’s team if he is to one day make it big in England.
He said: “Obviously you want to play at the highest level possible and being in the Scottish Premiership gives you the platform to do that.
“People are going to watch you if you are doing well.
“I need to keep doing well if I want clubs to come and watch me - so it’s down to me to make that happen.”
Manager Neil insisted he was “delighted” to have extended his top two players’ contracts but admitted they may never reach the end of the deals.
“If someone comes in with their chequebook you never know,” said the player/boss. “It was crucial to get the lads tied down.
“The chairman and the board at this club are really savvy when it comes to business. I don’t think any of our young players have walked out the door for free unless we have let them.
“To get the lads tied down for another three years safeguards us against that happening. We have invested a lot of time and money raising these guys as footballers.
“If they do move on, the money will help us to bring on the next generation of young players. If you look at the money we got for McCarthy and McArthur, we didn’t spend it on a marquee signing. It was reinvested into the youths and that is why we have got guys like Ali and Grant coming through.”
Accies may top the Premiership this term after 10 games but they were pipped to last season’s Championship crown by Dundee.
The sides will meet again at Dens Park on Saturday but Neil does not believe his side can learn anything from their four encounters last year.
“Both clubs have got different ways of doing things,” he said. “They have signed 14 or 15 new players, while we have mainly stuck with the guys who got us here.
“But it doesn’t mean both teams can’t have success. Dundee have been relatively successful for a team coming up and have started well.
“But I don’t think last season will have any bearing on the game whatsoever.”