The Guardian and Daily Telegraph had reported that Gillespie was set to leave the club at the end of the season to join Australia head coach and former Yorkshire batsman Darren Lehmann.
However, although he confirmed that he met Lehmann socially in Leeds on Sunday, Gillespie said he was not offered the role and is not interested in an international coaching job at present.
Lehmann had said recently on Australian radio that he wanted Gillespie as part of his backroom staff, fuelling speculation that the former pace bowler could be on his way.
“Darren Lehmann a while back on radio in Australia mentioned that he would be interested in getting me back into the Australian system,” said Gillespie.
“He is over here at ICC meetings in London and he thought he would make a detour to see his old mate in Yorkshire.
“I can confirm that he came to my place and we had a meal and a chat.
“He mentioned that there is a role coming up in Australian cricket, but I want to make it very clear there was no job offer from Darren.
“It was merely gauging interest.
“I informed him I’m not going to put my name forward and can end all the speculation right now.”
Gillespie, who combines his time coaching Yorkshire with the role of head coach of Big Bash franchise Adelaide Strikers, cited his young family as an important factor in his thinking.
“What you can’t get around is the travel,” he said.
“It’s well known I’ve got a young family, and do I want to be away 250-plus nights a year?”