The Briton sits 29 points behind his Mercedes team-mate in the drivers' standings with seven races of the 2014 season remaining.
Both men have been locked in a battle for the title since the beginning of the campaign, with their competitiveness evoking memories of the rivalry between Ayrton Senna and Alain Prost at McLaren in the late 1980s.
The pair's relationship became strained at the recent Belgian Grand Prix, when the pair collided, causing Hamilton to retire from the race.
Hamilton has vowed not to give up on his dream of becoming world champion for a second time ahead of the Italian Grand Prix on Sunday.
"The Italian Grand Prix is always a special one for me in terms of the memories I have there - going right back to my early career," he said on his official website.
"The karting championships used to race in Italy quite often and it's also where I met Nico - so that's where our rivalry really began. Monza is such a historic circuit and to win there is a really special feeling.
"I had that experience in 2012 and I'd love to do it again in 2014.
"Last season we really struggled at this race - but we have a fantastic car this year and I'm confident we can make up for it this time around. One thing I always love about racing at Monza is the fans.
"They're just so passionate about motorsport and the buzz around the place is unbelievable - particularly on the podium.
"Hopefully we can reward them with some exciting racing. My aim for the weekend, of course, is to claw back the gap in the drivers' championship.
"It's as big as it's been all season so I've got a lot of work ahead of me - but anything can happen in this sport. I won't give up until the flag drops in Abu Dhabi and there's still plenty of points to be won before then, so it's far from over yet."