The Scottish champions have been linked with the 25-year-old Denmark international for a number of months, and allegedly a club record fee of £11million has now been agreed with Bodo/Glimt.
After Saturday's 2-2 draw with AC Milan in a pre-season friendly at Celtic Park, O'Neill was asked if the deal was progressing.
"Yes, I'm hoping that that will happen," he said. "I think there's a good chance of it. But, until someone's actually signed and sealed, there might be things still up in the air, but it's certainly progressing", said the Scottish coach who also revealed that Hogh was about to have a medical in Glasgow.
"Yes, apparently so. He will have one in the next 24 hours, I think."
Hogh came through the youth ranks with local club Randers but was sold to second-tier Hobro after an injury-hit spell, including a loan to Valur in Iceland. He then signed for AaB in January 2022, but just a year later, he moved on to join Stabaek on loan, a club that had just been promoted to the Norwegian Eliteserien.
From then on, Hogh has been on fire as Stabaek turned his year-long loan into a permanent contract after he scored eight goals in 14 games.
Hogh then signed a pre-contract agreement with Bodo/Glimt to join their top-flight rivals in January 2024. He instantly became a hit as he finished the season as the leading goal scorer with 12 goals as they retained the Norwegian title.
He was also the club's leading goal scorer the following year with 17 goals, and in January this year, he scored two goals in a 3-1 win against Manchester City. The following week, he found the net again in a 2-1 win away to Atletico Madrid.
Hogh was first called up to Denmark's senior squad in March and in his second appearance came off the bench to head Denmark's equaliser in their World Cup play-off final against the Czech Republic.