The former Republic of Ireland international has dropped behind Brad Guzan in the pecking order this season, making just two Premier League and two Carling One Cup appearances in the first team.
The 36-year-old has been linked with a loan move to Championship side Hull, but Lambert is adamant that Given will stay at Villa Park.
He said: "Has there been any interest in Given? I haven't a clue. Honestly, I've not had that conversation and he hasn't said. I'm just happy to have two quality goalkeepers here.
"Am I tempted to send Given on loan? No, I wasn't tempted. You need the two of them to push each other.
"The fact Brad has got Shay breathing down his neck, I'm sure is driving him on."
Given still has three-and-a-half years remaining on his Villa contract, while American Guzan signed a three-year contract in the summer.