Archibald had two previous bids turned down by KPMG who said they were a long way short of the club's estimated valuation.
The former Scotland international submitted his final bid, along with two others before the deadline on Monday.
But provisional liquidator, Blair Nimmo, has confirmed that the Archibald offer has become the favourite to receive the backing of KPMG when they put it before the club's creditors.
Archibald had two previous bids turned down by KPMG who said they were a long way short of the club's estimated valuation.
Mr Nimmo said: "We are delighted that, whilst there is still some way to go, we will very shortly be able to move the process onto the next stage and hopefully conclude a deal which will ensure the survival of the club and see it playing in the first division next season.
"The assistance of a great many people, in particular the staff, players and fans, allowed us to keep the club trading during a very difficult period.
"I would like to take this opportunity to thank them for their support, which has been invaluable."
Archibald has been in discussion with a number of different parties who could have an influence on the outcome, in order to find the best way for all concerned.
The bid would still be subject to approval by the creditors and the resolution of title ownership of the ground.
It would then take between four and six weeks to conclude the deal, but matters will be moved forward as quickly as possible.
Archibald admits that he is eager to secure the ownership of the Diamonds as soon as possible.
"It might take four to six weeks to put the paperwork together and put things in action," said Archibald.
"We are keen to get things established because then we can get in there and start doing something.
"The season has just finished but the new season will soon be upon us. At the moment all we can do is wait and see."