Rangers are on the hunt for a new manager following the departure of Pedro Caixinha in October.
Graeme Murty has been in charge of the Rangers first team since then, with the Gers also recently failing in their pursuit of Aberdeen boss Derek McInnes.
Kilmarnock central defender Greer has suggested that Rangers should have made a move for his manager Clarke before he was appointed in the current role.
The 54-year-old former West Bromwich Albion and Reading boss was appointed the Kilmarnock manager in October 2017.
When asked if Rangers had missed an opportunity to bring in a top-class manager, Greer told Herald Scotland: “Definitely. I think so. The gaffer has got fantastic pedigree.
“He has worked with some of the biggest clubs in England and with some great clubs and top players as well.
“When we appointed Steve Clarke here we were as surprised as anybody. It is a great appointment and credit to the club for it.”
Greer added: “Rangers is one of the biggest clubs in Scotland, but if you look at the clubs he (Clarke) has worked with down in England you can see he has worked with some of the top clubs down there. I don’t think he would have been fazed by it at all.”
The Daily Record quotes Ardley as saying when asked if Rangers have an option to sign break the loan deal in January: “The honest answer is there probably is.
“But I’m not sure it is going to happen, I’m pretty confident something is not going to happen. Most season-long loans have these sort of things in there but it is not something to really worry about.”