Director of rugby Richard Cockerill said: “Toby rang me and said he has decided to go and do other things. I suspect probably in France.
“He is our club captain, and he will be our captain until the end of the season. There is a long way to go and a lot of things to do.
“We have had lots of situations where guys move on and the good ones, and Floody is certainly one of the good ones, make their decision and concentrate on playing and we will try to win the Aviva Premiership and do what we can in the Heineken Cup.
“Floody has been great for us and he will continue to be great for us for the rest of the season.”
Flood, 28, made the 99th starting appearance of his Tigers career in the win in Montpellier last Sunday.