Speculation about Oliver's playing future ramped up again last week after Demons chief executive Gary Pert reportedly made contact with multiple clubs to test interest in a potential trade.
Oliver, who has six years left to run on his lucrative contract, then met with Geelong officials and players.
But as the AFL trade period officially opened on Monday, Lamb rejected suggestions Oliver could leave the Demons before the October 16 trade deadline.
"Our position has never changed. We've never been trading Clayton and we won't be," Lamb told reporters at Marvel Stadium.
It is the second time in as many years the Demons have floated Oliver's name and then held him to his contract.
But Lamb denied Melbourne had mismanaged the 27-year-old, who has also battled personal issues in recent years.
"I think the work we've done with Claz and the work that Claz has done himself has been outstanding," Lamb said.
"He's obviously had a couple of challenges over the journey. He's got himself into a really good spot."
Melbourne list boss Tim Lamb insists the Demons haven't mismanaged Clayton Oliver. (James Ross/AAP PHOTOS)
Lamb sidestepped questions about Pert discussing Oliver with rival clubs.
"There's always conversations at this time of year and I'm not going to go into the details of who spoke to who," he said.
"But clubs ring us, we ring clubs. It doesn't mean that someone's going to be traded."
Geelong list boss Andrew Mackie on Monday said there "was some chatter that Clayton might need to look at something else" before the midfielder met with the Cats.
But Mackie was noncommittal on trying to do a deal for Oliver during the trade period.
"We're talking hypotheticals now. From that point of view, I don't like to delve too far into it," Mackie said.
"We haven't spent too much time on it ... we look at all sorts of things and opportunities. It's not just Clayton."
Melbourne have also faced questions this year over star midfielder Christian Petracca, who considered his future at the club before confirming he would stay.
There has also been speculation about Kysaiah Pickett's playing future, but Lamb shut down talk the contracted livewire could request a move during the trade period.
"Yeah, no. Kozzy's playing for us," Lamb said.
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