Red Bull finished third overall last year while Renault were sixth and McLaren, then with unreliable Honda engines, a distant ninth.
Both Renault and McLaren are tipped to make big improvements but Red Bull have looked stronger in testing and Verstappen made clear on Thursday that his focus was on Ferrari and champions Mercedes.
"You pay attention to everybody, but I don't think they will be our main rivals," the 20-year-old Dutch driver told reporters at the Circuit de Catalunya when asked about the other Renault-powered teams.
"And we don't want that to be the case as well, because that would mean we are not doing such a good job. We need to look (at those) ahead."
Verstappen won two races last year while Australian team mate Daniel Ricciardo was also triumphant in Azerbaijan.
The team, who last won a title in 2013 with Sebastian Vettel, have sounded increasingly upbeat about their car as testing has progressed.
Ricciardo will be out of contract at the end of the year and has been linked in media reports to both Mercedes and Ferrari for 2019.
Red Bull, who have Verstappen signed up to the end of 2020, want to keep the Australian in what is one of the most exciting pairings on the starting grid.
The energy drink brand's motorsport consultant Helmut Marko told Sky Sports television that a time frame had now been decided.
"We agreed with him a deadline," said the Austrian. "So as soon as this deadline is over we'll tell you if it's yes or no."
(Reporting by Alan Baldwin, editing by Ed Osmond)
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