Gravesen's agent John Sivebaek told Danish television station TV2 that the former Real Madrid and Everton man will turn down any overtures from Sheffield United.
"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."
