In-form Napoli are just four points adrift of Roma heading into Saturday's trip to Palermo at Stadio Renzo Barbera, having won four successive league matches.
Napoli - inspired by Gonzalo Higuain's three goals in that period - have accounted for Lazio, Genoa, Chievo and Udinese to close the gap on Roma after 22 rounds.
And Callejon sees no reason why Napoli cannot secure a top-two berth ahead of the Romans.
"We believe in second place, and we're not giving up," Callejon told Radio Kiss Kiss Napoli. "We will try to do our best in every competition, there are still many games and we hope to do well with every race.
"We have won four games in a row in the league and we're going to Palermo trying to stretch the strip. It will not be easy but we're fine and we can express ourselves to the maximum.
"We have to play as we are doing in the last few months and still improve in front of goal trying to realise all the opportunities we create."
Roma are back on home soil for their hosting of cellar-dwelling Parma on Sunday.
They were 2-1 winners at Cagliari last week, a result that ended a run of four consecutive draws.
On-field matters appear to be the least of Parma's worries, with the club facing possible bankruptcy due to outstanding debts.
Serie A pacesetters Juventus are also in action on Sunday.
The runaway league leaders will make the trip to second-bottom Cesena in the midst of a 13-match unbeaten streak in Serie A.
Juve have kept seven clean sheets in that period, while Argentina international Carlos Tevez has scored eight goals.
European hopefuls Fiorentina and Sampdoria - fourth and fifth respectively but level on 35 points - are both on the road this weekend.
Fiorentina and Sampdoria occupy the two UEFA Europa League spots heading into their trips to Sassuolo (Saturday) and Chievo (Sunday).
Lazio will be monitoring those matches closely, with the Rome-based outfit a point adrift as they prepare to play Udinese away from home.
After ending a run of consecutive defeats against Palermo last week, Inter will be hoping for consistency when they visit lowly Atalanta.
City rivals Milan, who welcome Empoli to San Siro, are also in need of a consistent run of results after losing to Juve last time out - their third defeat in four matches.
Elsewhere, Torino go head-to-head with third-bottom Cagliari, while high-flying Genoa tackle Hellas Verona.
