The former Republic of Ireland goalkeeper has fallen behind American Brad Guzan in the pecking order at Villa Park after a number of high-profile mistakes at the start of the campaign.
The 36-year-old still has three-and-a-half years left on his contract after moving to the Birmingham outfit from Manchester City in 2011.
And Lambert is happy with his current goalkeeping options, with the Villa manager insisting Given still has a role to play at the club.
“Has there been any interest in Given? I haven’t a clue. Honestly, I’ve not had that conversation and he hasn’t said,” Lambert 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.”
Get 8/1 enhanced odds on Tottenham to win or 11/1 enhanced odds on Liverpool to win at White Hart Lane on Saturday afternoon. Click here to sign up now. T&Cs apply.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news