Ms Jones told BBC Radio Wales she did not want to give up being an AM to go to Brussels to replace Nathan Gill, UKIP Wales leader.
Mr Gill has been told by the UKIP assembly group and the UKIP party chairman Steve Crowther to stop "double-jobbing" as an AM and MEP.
Mr Gill said those making such calls were doing it out of "malice".
"We've got Brexit now and I think that, possibly, it may be best to leave that role unfilled," Ms Jones told the Good Morning Wales programme.
"I'm surprised I've not been formally asked what I'd like to do."
Ms Jones, the South Wales West AM, is one of two people who could take up the role of UKIP Wales MEP if Mr Gill made it vacant - the other being South Wales East AM David Rowlands.
She would, in theory, have first refusal over Mr Rowlands as she was third in the 2014 UKIP European Parliament election list and Mr Rowlands was fourth. The number two candidate, James Cole, is no longer in the party.
Asked if she would give up her position as AM to become an MEP, she said: "No I wouldn't. I'm not interested. Since becoming an AM I've thrown myself totally into what I'm elected to do.
"They'd have to ask David Rowlands obviously but neither of us have formally been asked, although David may say 'oh no I'm settling in in his role', and he is actually, he's doing very well.
"Quite frankly I think it's impossible to do two jobs, especially when one is in Brussels and Strasbourg and the other is in the Welsh Assembly. It's a very difficult situation."

The two small eels were found in a routine fish survey on the River Tud, a tributary of the Wensum in Norfolk.
Increased numbers have also been seen at the New Mills fish pass in Norwich, which was installed eight years ago.
The Environment Agency, which monitors numbers, said it was encouraging but did not "herald the recovery of the species as a whole".
Jez Wood, a specialist at the Environment Agency, said the discovery of the eels on the River Tud was important.
"Two doesn't sound like many, but these are the only small eels we've found on this stretch for years," he said.
"While this does not herald the recovery of the species as a whole, it does show the positive benefit of eel passes at barriers to migration."
The status of the European eel is regarded as "critical", and globally the population has fallen over the past 40 years, with numbers down by as much as 95%, the Environment Agency said.
Barriers to upstream migration is thought to be one of the reasons for the decline.
These reduce access to the freshwater habitat preferred by eels while they mature.
In Norfolk, the Environment Agency is creating passes at several key obstruction areas on rivers to help increase numbers.
It said numbers in Norfolk rivers rose to a record of 34,000 in 2009 after a pass was introduced at New Mills Yard, in Norwich.
UKIP's Welsh MEP post may be better left unfilled as a result of Brexit, party AM Caroline Jones has said.
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Eels have been found in a stretch of river where they have not been seen for nearly 40 years.