"Our natural born rivals are right ahead of us," Howard, 32, told BBC Radio Merseyside.
"We're going to try and nip on their heels and get a couple of results. For the city this run-in will be great to see and we'll try to overtake them."
He added: "I think we've still go miles to go and we want to keep cracking on. I'm sure they're going to do all they can to crack on up the table as well."
Everton travel to Wolves on Saturday, who are in the middle of a relegation scrap, and the United States international says the battles in all areas of the table are what separates the English game from other countries.
"That's what makes England beautiful and the Premier League so amazing," Howard continued.
"There's cup finals everywhere you look and people are trying to fight off relegation, get into the top half of the table, get into Europe and win the league.
"No team can go 'alright we've five or six games left and we'll cruise'. It's impossible to do that."
Source: BBC Sport
Source: BBC Sport