Unless a meeting is called, the trustees won't have another chance to make an official offer before the Texas board makes a decision.
Richmond County's board has met twice in closed-door sessions to discuss offering a new contract to Bedden, whose contract ends in July.
Some board members said after Tuesday's meeting that an unofficial offer was made last week.
"We've not voted in public on one, but he's got an offer in his possession," member Jimmy Atkins said after the meeting. He divulged no details.
Board member Helen Minchew said Bedden was offered a raise that would be deferred until employee furloughs or layoffs end. That would likely mean waiting for an economic recovery to boost tax revenues.
Board Vice President Alex Howard said the offer was made Feb. 10 but that there has been no response from Bedden. Board member Eloise Curtis also confirmed that offer.
Minchew said the board would like for Bedden to agree to the terms before it votes to make an official contract offer. That didn't happen Tuesday, but she said the board is supposed to meet again on the matter Monday.
"I think it's still there," she said of the unofficial offer.
After Tuesday's meeting, Bedden wouldn't speculate on his future but did say that the longer his contract issue lingers in Augusta the more it becomes a distraction.
"I would like for there to be closure for the school system," he said.
In other action, Bedden told the board he would like to hold off until April 13 to decide whether teachers and others will have to take an additional three furlough days, as Gov. Sonny Perdue recently recommended. Bedden said the school system could collect $2 million more than budgeted in tax revenue, partly because of stronger enforcement by the tax commissioner's office.
He said the extra property tax revenue could nearly offset the $2.4 million the three furlough days represent.
If the furlough days become necessary, Bedden has recommended they be taken April 30 and May 24 and 25.
In that case, the system would need a waiver from the state to allow it to have three fewer school days. Students would still be attending class the required number of hours for the year.
Bedden said delaying the decision could spread the pay cut out over a shorter period of time but that approving the furloughs now could reduce workers' pay needlessly.