"They are just playing in the Championship. Thomas wants to stay at Celtic and fight for his place as we have stated all the time."
Meanwhile, Gravesen's team-mate Jiri Jarosik will also stay with Gordon Strachan's men, despite a disappointing season for the Hoops.
Jarosik told Czech daily Pravo: "Celtic are a massive club and I would not like to make a step down.
"I believe that I can win a place in the starting line-up even though there is, I guess, 12 midfielders.
"I am 29 and I would like to play two or three years for such a big club like Celtic. Only then would I consider a move to a country where I could win the fifth title."