Now 27, Agbonlahor has been with Villa for over 15 years, breaking into the first team in 2006 at the age of 19.
Although contracted to the end of next season, Agbonlahor is already thinking of signing another extension to take him into his 30s, and potentially to the end of his career.
Agbonlahor said: "It is hard in this league to be a one-club man, but it's always been on my mind to play for Villa until I retire.
"It feels weird even thinking about putting another shirt on.
"The club has high hopes and we are building the squad. Look at the facilities, fan base, Villa Park and the training ground - there's no reason why you would want to leave."
Lambert showed over the summer he is willing to retain his players without letting their contracts run out after getting Ciaran Clark, Andreas Weimann, Nathan Baker and Ashley Westwood to sign new deals.
Although eager to stay with Villa, Agbonlahor may have to wait until next summer before he gets the opportunity of putting pen to paper on another contract.
When asked about Agbonlahor being a one-club player, Lambert said: "It's pretty rare now. There aren't too many around.
"I know Gabby has been here a long time, and when you look at the next 20 months that's also a long time in football.
"In years gone by you wouldn't find out what was happening to you until a week before the end of the season.
"Then all of a sudden it goes full circle and it becomes 20 months, two years (prior to the end of a contract when a player signs a new deal). It's just strange in football.
"I understand what he is saying, but there is a long, long way to go before there's anything on that. The end of season is the time to look at these sort of things."
Of greater concern for Lambert now is Agbonlahor's fitness as he is currently sidelined with an ankle ligament injury and is due to miss Saturday's Barclays Premier League clash at home to Cardiff.
"He's obviously enjoying his football, although his injury is a bit frustrating at the minute," added Lambert.
"The important thing for me is for him to get his ankle sorted and come back fit."