The Bolton boss met on Saturday with Sharon Brittan of the Football Ventures consortium, who administrators made preferred bidders for the club four weeks ago.
The London-based businesswoman, who is likely to take a top post at Wanderers if a deal is struck, also spoke to senior players at the team hotel in Wycombe to allay concerns about delays.
Rumours persist that alternate parties are waiting in the wings for a chance to buy both the club and hotel, a queue which is understood to include the owners of online fashion retailer Boohoo.com.
Parkinson gave an update after the Wycombe game, however, which indicated the Football Ventures consortium were within touching distance of becoming the new owners.
“We spoke today with the prospective owners and she said it was very, very close to being done,” he told The Bolton News.
“When anyone says that to us there’s a wry smile because we’ve been here so many times before. We understand it’s an incredibly difficult deal. Two separate administrators, such a complex scenario.
“But we have got to make sure there’s a Bolton Wanderers ready to compete in this season and I am sure there will be.
“Sharon came in and had a chat with the players and that alone lifted the lads because having that communication is great.
“I have met her a couple of times and all I can say to our supporters is that she’ll be incredible for Bolton Wanderers, going forward.
“I think it will be a good thing for the club and for the town.
“Let’s hope she can get the deal done.”