Lambert knows keeping hold of the pair and other key players is vital as part of his long-term project to rebuild Villa - and he has the backing of club owner Randy Lerner.
It will be a reversal of Villa's trend in recent seasons of selling leading performers such as Gareth Barry, James Milner, Stewart Downing and Ashley Young.
Benteke has scored 17 goals since his £8million move last summer from Genk and the Belgium international has been linked with a host of clubs.
Weimann has netted 11 goals in his first full campaign of top-flight football and has been offered a new deal by Villa.
Lambert said: "Do I think Weimann and Benteke will be at Villa next season? Yes, yes. I think they want to be here. I've spoken to the lads as well and they've been great with it.
"There is no point in trying to build something if it (players) keep on going away. There is no point in coming in for one year and, after that, the lads go away again.
"I don't think that is building for any sort of future. Do I have the final say on it? Oh yes. I've got to - but Randy (Lerner) has been great with me.
"Everyone knows the situation. If players do well, then teams speak about them. Everyone knows the situation. Whether it is true or not or agents fabricate things remains to be seen.
"When I first came in here, we sat down and explained what I thought. Randy was right behind it, no problem at all.
"He has been excellent with us. There is no point in building something, if a year later it (a player) goes. I don't want to go back to square one."
- Sports & Recreation