Chavez, who has called Bush "the devil", "a donkey" and 'Mr Danger" has accused the US of plotting overthrow him.
McCain has, in turn, described Chavez as a dictator who wants to emulate Fidel Castro, the retired Cuban leader.
Chavez warned that McCain represented the same mentality that characterised the "terrorist" Bush administration.
The Venezuelan leader said he had better communication with the administration of Bill Clinton, the former US president.
"Independently of who wins the elections, we are hopeful and it is within our plans to enter an era of better relations with the US government," he said.
"At the least one would hope for the level of relations we had with ex-President Clinton."
He did not mention Democratic hopefuls Barack Obama or Hillary Clinton.
Both are cautious about Chavez, although Obama has said he could meet him.