The Manchester City striker had a previous loan spell at Celtic Park in 2005, and spent last season on loan at hometown club Cardiff City.
"There have been conversations between both clubs," said Celtic manager Neil Lennon.
"I didn't speak with City, but the two clubs have been working on that in the background."
Both sides have been in Dublin recently taking part in the Dublin Super Cup, which Manchester City won on Sunday after beating Inter Milan 3-0.
With an abundance of strikers at Eastlands, Blues manager Roberto Mancini is open to the loan deal.
"If Celtic want Craig... he can go. Craig is a good striker and he can play at Celtic, because they're an important team," Mancini told BBC Sport.
The Welsh international striker has had previous spells at nine different clubs, including Liverpool, West Ham United and Newcastle United.