Megson, in temporary charge since the sacking of Tony Pulis, watched as West Brom drew 2-2 at home to Newcastle United on Tuesday despite leading by two goals.
He also took charge at the weekend when his side drew 1-1 at Tottenham Hotspur.
Former Newcastle and Crystal Palace manager Alan Pardew is reported to be in the running for the job.
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"You can probably enlighten me," Megson said when asked whether he knew what the future held. "The chairman has come down as he always does and he says he wants to natter at 10 o'clock tomorrow and that's as far as I know.
"He didn't say why but I wouldn't expect him to, that's the club's business. All I can say for definite is that I am meeting the chairman tomorrow."
Megson had a four-year stint in charge of West Brom from 2000-04 and said he has enjoyed being back in the hot seat, even if it turns out to be a brief spell.
West Brom fans sang his name on Tuesday.
"I thank the fans for that. It was like going back 14 years. It was terrific but what wasn't terrific was the result," he said.
Goals from striker Hal Robson-Kanu on the stroke of halftime and winger Sam Field looked to have given West Brom a priceless win that would have give them some breathing space.
They did move up to 16th with a point but were left to rue Jonny Evans' own goal that stretched a long winless run.
"We scored two really good, well worked goals, we are supposed to be a big side at set pieces but we conceded awful goals for us to give away," Megson said.
"We have to pick ourselves and go again."
Newcastle avoided a fifth successive defeat.
"I was upset, but the reaction of the players, their workrate -- these players care," Newcastle manager Rafa Benitez said.
"They will try. In terms of effort they were really good."
(Reporting by Martyn Herman; Editing by Greg Stutchbury)
