The pair made no secret of their intense rivalry and at times open dislike for each other when they were team mates at McLaren last year and Alonso's departure to Renault has added a new dimension to their feud.
Australia's Red Bull driver Mark Webber believes their rift could even spill on to the track as both drivers try to prove a point.
"There was plenty of spice last year, a bit of a lovers' tiff between Lewis and Fernando Alonso within the same team," Webber wrote in a column for the BBC Sport Web site.
"I think the championship could be more fiery this year. It could actually get nastier in terms of the battle on the track because the gloves are off as two of those players are in different teams."
Alonso and Hamilton both played down the suggestion when they appeared together at a news conference in Melbourne on Thursday, trading compliments instead of insults.
Hamilton, who recently said he expects McLaren to be a far more harmonious team now that Alonso has departed, said it had been an honour to work with the Spaniard last year, when he was asked in jest whether he would miss him.
"When you have a two-time world champion (Alonso), when you come into your first season and someone you've been watching for so many years, you come and you work against them, work with them, it's a privilege," Hamilton said.
"From that point of view, it's a shame he's not there."
The 23-year-old Briton said he had already developed a strong relationship with his team mate Heikki Kovalainen and believed he could pick up some tips from him even though both are relative newcomers to the sport.
"It's a new challenge for me and Heikki. Having another guy in the team, you always learn something new from a different driver, so I've got that opportunity," Hamilton said. "He has got a great career under his belt already, lots of experience as have I.
"Both are coming into our second year in Formula One and we both have the same hunger for winning and pushing the team forward. I think it is quite good that we are both aiming in the same direction."
Alonso, who joined McLaren after winning the 2005 and 2006 world titles with Renault, returned the compliment to Hamilton, saying the Englishman's raw enthusiasm had inspired him.
"When I changed and I joined McLaren, Lewis was arriving in the team as well as new in Formula One, so always giving fresh ideas and a fresh way to do things and you always learn from everybody," Alonso said.
"We are not together but we are still racing each other in different teams...it's a new challenge."