Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
The Sky Blues opened initial talks with the 28-year-old back in the autumn but the midfielder has rejected the deal after the club's relegation from the npower Championship.
Clingan joined Coventry from Norwich in 2009 and has gone on to make a 100 appearances during his time at the Ricoh Arena.
"I have spoken to Sammy, we have offered him a decent contract but he chose to turn it down, but that's his prerogative," manager Andy Thorn told the Coventry Telegraph.
"He's been great but it's highly unlikely that we'd have got anywhere near what he was asking for.
"We offered him a decent deal and he chose to wait until the end of the season and see what he can do so we wish him all the best."