The Ladbrokes Premiership club have reportedly rejected a bid of around £3million from the Blues for the 34-year-old who signed for the Hoops in 2014 after two years out through injury.
However, Brown wants Gordon, who has also won his place back in the Scotland set-up, to remain with the Hoops.
He said: “Craig is fantastic. He has shown that this season.
“He has come back pretty much from the dead to be our player of the year last year.
“It is frightening, he can go for another few seasons as well.
“He is enjoying his football here and hopefully he stays for a long time.
“The gaffer wants him here, the club and all the lads want him here so it would be great for him to stay here but it is understandable that people come in for him because he has been playing top class all season and has stepped up from last season.”
Brown, meanwhile, has targeted another 200 appearances for Celtic.
The 31-year-old Hoops skipper reached the 400-mark against St Johnstone in midweek.
Ahead of the visit of Hearts on Sunday, he said: “The gaffer has said I have a couple of hundred more so I better try to stay fit and continue.
“I want to stay here as long as I can and win as many trophies as I can.
“At 34/35 you can still play, especially here in Scotland.
“There have been a lot of players who have played to 37/38 up here so I will try to push my body as far as I possibly can but I need to look after it on the pitch and off the pitch.”