Lehmann, the Australia head coach and former Yorkshire batsman, has made his friend and former team-mate his No 1 target.
But Gillespie has said that the job to replace Craig McDermott is “not something that I’m coveting”.
He made clear: “As in any walk of life, if someone rings you up, you listen to what they have to say, but I can assure people that I’ve got absolutely no intention of going anywhere.”
Gillespie’s commitment to Yorkshire cannot be doubted, but Lehmann has made no secret of his desire to bring him on board.
Speaking to an Australian radio station yesterday, Lehmann said: “Gillespie will certainly be at the forefront with other bowling coaches.
“We hope we can entice him back.”
Australia are not expected to name McDermott’s replacement before the start of their domestic season this autumn.
Theoretically, it would pave the way for Gillespie to link up with Australia at the end of the English season, by which time he hopes to have led Yorkshire to a hat-trick of County Championship titles.
However, Gillespie also has a contract with Adelaide Strikers, the Big Bash franchise that he coaches during the English off-season.
It also remains to be seen whether Gillespie would be tempted by a lesser international position; after all, he was favourite for the England head coach’s job last year before it went to his fellow Australian Trevor Bayliss.
Gillespie, 41, is ambitious, however, and it is a reflection on the work he has done at Yorkshire that he is invariably linked with any coaching position that comes up at international level.
This is his fifth season at Yorkshire, whom he may feel that he has taken as far as he can in a County Championship sense, although the club certainly have room for improvements in one-day cricket, something that he is determined to address.
The biggest consideration for Gillespie, however, is his wife and four children, who are happily settled in Leeds.
When he was linked with the England job last year, he often spoke of the potential difficulty of spending long periods abroad with a young family to consider.
On the other hand, circumstances change and Gillespie could see the Australian job as the stepping stone to a head coach’s role at international level.
The only certainty is that he is one of the hottest coaching properties around.
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