A BBC spokesman refused to comment on any developments, saying: "As we said last week we have an investigation ongoing and we won't comment further until that is concluded."
Spokesmen for Tymon and Clarkson also declined to comment.
Meanwhile, a petition to Bring Back Clarkson has attracted more than 960,000 supporters.
Another petition calling on the BBC to hire Alan Partridge, the fictional broadcaster played by Steve Coogan, as the new presenter of Top Gear has also been launched, with almost 20,000 signatures.
The BBC has postponed the remaining episodes of Top Gear following the fracas, which has seen it lose millions of viewers and receive thousands of complaints.
Sunday night's planned episode was replaced by a Red Arrows documentary which pulled in just one million viewers - compared to the five million who regularly tune in for the popular motoring show.
ON Tuesday the BBC Trust ruled that Clarkson was not being racist when he used the word "pikey" on Top Gear - a decision which has sparked condemnation from the Traveller Movement.
The presenter put up a placard with the words Pikey's Peak on the BBC2 series in February last year.
But the Trust's Editorial Standards Committee (ESC) concluded that the word had been used to mean "cheap", rather than as a term of racist or ethnic abuse.
A spokesman for the Traveller Movement rejected the decision, saying: "We are horrified by the BBC's green lighting of the use of the word 'pikey' by the Top Gear presenters."
Clarkson raised more eyebrows this week when it emerged that in his column in Top Gear magazine, he discussed immigrant taxi drivers in London, saying that their cars smell "faintly of lavender oil and sick".
The presenter is still scheduled to appear alongside co-hosts James May and Richard Hammond at four live Top Gear shows in Norway on March 27 and 28 and a decision on whether to go ahead is expected soon.
All three men's contracts expire three days after the Norway gigs, which could render any disciplinary hearings redundant.
Clarkson is also expected to record an episode of the BBC's top-rating satire show Have I Got News For You in May.
-AAP