Celtic signed Brown from Hibernian in the summer of 2007 for a transfer fee reported by The Scottish Sun to be worth £4.4 million.
McCoist was working as the assistant manager under Walter Smith at Rangers at the time, and the Scotsman has revealed that the Gers tried to secure the services of the 32-year-old Scotland international midfielder.
“He has had a great season and he has been a great player for Celtic over the years,” McCoist, who managed Rangers from 2011 until 2014, told The Scottish Sun about Brown.
“I remember that we tried to sign him at Rangers. He seems to have recovered well from that mistake!
“I’m joking obviously. He is a smashing boy as well and looking back over his ten years with Celtic, he has been remarkable.”
Brown is one of the best midfielders in Scotland and remains an important player for Celtic despite being in his early 30s.
The 32-year-old has developed and improved massively since his move from Hibs to the Bhoys, and is a force to be reckoned with in midfield.
During his time at Celtic Park so far, the Scotsman has won the league title seven times, the Scottish League thrice and the Scottish League Cup on three occasions.
Celtic will be aiming to win the Scottish Premiership, the Scottish League Cup and the Scottish Cup this season.