The double winners' chairman Tony Rowe has stated than any approach by the Rugby Football Union for Baxter would be rejected and the director of rugby has followed suit by confirming his allegiance to Sandy Park.
England's worst Six Nations performance is being reviewed with the findings due next week, placing Jones' position as head coach under scrutiny.
There is strong support for Jones at Twickenham on the basis of his winning record of 77 per cent and historical achievements, including reaching the 2019 World Cup final, but if he was to depart Baxter would be the leading domestic candidate to replace him.
"That is exactly my view - I'm under contract, I'm happy here and that is my biggest consideration," said Baxter, whose deal expires in 2023.
"If you were at the club here now and I just walked up to the media room, I'm looking down at one end of the ground and I'm seeing a pretty impressive hotel being built that is going to be finished before Christmas.
"Across the ground now we are moving one of our terraces because they have started working on building a new grandstand with 2,000 premium seats to rival the grandstand this side.
"We are going to be able to have a 15,000 capacity before Christmas with some fantastic facilities available, both overnight in the hotel, in seating, in the hospitality here at the club.
"It's an exciting time to be part of Exeter, it's an exciting time to be part of the drive to make this club something very special.
"I have played my part in that so far and there is a lot of attractive reasons to carry on playing my part in that. That would very much be my take on it at this stage."
If the RFU does decide to part ways with Jones, it will only be required to pay out the notice period on his contract, which expires after the 2023 World Cup.
This notice period can be activated by either party at any time and this clause in the contract means it would not be prohibitively expensive to part company with the 61-year-old.