"We'll see if I keep him on my birthday list," Australian Ricciardo smiled.
"We both said at the start of last year that it would be a good problem to have -- if we're both fighting at the front and having some battles," he added.
Ultimately, Mercedes and Ferrari got the early jump on Red Bull last year, but the former title-winning team is confident it can get a stronger start to 2018.
And Ricciardo said he and Verstappen can deal with any tension that might bring.
"If it's ultimately deciding a world title we would happily run with that challenge," he said.
"I believe this year we will close the gap. Is it enough to fight for a title? I think we can certainly get close but we'll see."
If he does have a better car, Ricciardo acknowledged that he will also have to deal with an ever-improving Verstappen.
"Max improved from 2016 to last year," he admitted. "I won't say he came a long way because he was always there but he certainly improved and I think next year it's going to be a lot of fun."
And he says he has some of his own improving to do as well.
"I had some great races, but obviously I would love all 20 to be great and not all 20 were," said Ricciardo.
"Obviously I give every year a good crack, but (I want to) give this year a proper crack. I was pretty pleased with last year but I've still got some improvements to make."