One source said Georgia Tech could finalize a deal with Pastner on Friday.
Pastner, 38, took over after John Calipari left seven years ago and has taken the Tigers to the NCAA tournament four times in his tenure. However, Memphis has not played in the postseason the past two years.
Memphis announced last month that it would stick with Pastner, with university president David Rudd and athletic director Tom Bowen saying in a statement that the school would "make the necessary investments and changes" so it could "compete at the highest level."
Pastner has a 167-73 record at Memphis, but the Tigers have gone a combined 37-29 the past two seasons. They went 19-15 this season and lost 72-58 to Connecticut in the American Athletic Conference championship game.
Pastner averaged more than 24 wins over his first six seasons. His 148 victories at that point made him the ninth-winningest coach in Division I history for his first six seasons. He joined Calipari as the only Memphis coaches to win 18 or more games each of his first six seasons.
Pastner also coached the Tigers to the NCAA tournament four straight years (2011-14), something only Dana Kirk (1982-85) and Calipari (2006-09) managed at Memphis.
Memphis hasn't been back to the tournament since. The Tigers' home attendance average dropped from more than 16,000 during Memphis' last NCAA tournament season of 2013-14 to 11,812 this season.
Rudd and Bowen said the men's basketball program "operates in a manner consistent with the core values of our university and community but has fallen short in our on-court performance the last two years."
Gregory, meanwhile, was fired last week by Georgia Tech.
"At the end of the day, the evaluation for me came down to what does the future look like," athletic director Mike Bobinski said. "Do we in fact have a clear path forward to greater success and higher levels of success in the years ahead, and my determination was, I didn't see it. I ultimately didn't see it and ultimately led me to the decision that we needed to make a change."
Gregory, 49, replaced Paul Hewitt in 2011 and did not take the Yellow Jackets to the NCAA tournament during his tenure. He was 76-86 overall and 27-61 in ACC play.
Georgia Tech finished 21-15 overall and 8-10 in the ACC this season. The team made the postseason for the first time in Gregory's five seasons, winning two games in the NIT before losing in the quarterfinals.
Bobinski said the team's failure to make the NCAA tournament factored into his decision.
"It's hard to deny that would have given us a different thought," he said in a news conference.
Georgia Tech will owe Gregory more than $1.3 million for the final two years of his contract. Hewitt, who took a $7.2 million buyout after he was fired in 2011, is still owed $2.7 million from the school over the next three years.
The Associated Press contributed to this report.