The Toffees goalkeeper refuses to give up hope despite conceding it is unlikely that the Merseysiders can overhaul the three London clubs also in the Champions League hunt.
The 34-year-old is refusing to give up hope on a top-four finish in the Premier League despite the Toffees trailing fourth-placed Arsenal by five points.
A run of five wins in the last eight games has kept David Moyes' side in touch and Howard says anything is possible.
"I think we've always been a dark horse, we've always been the outsider in that race, and we still are," he told Sky Sports News.
"If we put a few moments of magic together, if we can win out - which is never easy with the games that we have - and we can get some help in and around us, anything is possible."The Toffees make the short trip to Anfield on Sunday for the Merseyside derby against a Liverpool side buoyed by a 6-0 thumping of Newcastle last time out.
Howard is wary of Brendan Rodgers' side after it showed it can cope without the suspended Luis Suarez, but is confident Everton can end its long wait for a win at Anfield.
"All the talk has been about how Suarez has carried them, maybe rightfully so, but boy have they made a statement and shown everybody that they also can find goals from other places," he said.
"They are a threat, we know that, and I think we'll have mapped out a plan to try and beat them come Sunday."