Hamilton pipped his rival to the championship last season to claim his fourth world title.
The Briton has reigned victorious in three of the last four seasons after Vettel won his four championships in consecutive years.
The two racing drivers have dominated the sport for the past nine years and they are once again favourites heading into the 2018 campaign.
Vettel’s and Hamilton’s rivalry often boiled over in races last year with the two clashing at the Mexico Grand Prix when the former drove into the back of the Mercedes driver, causing both of them to pit.
But Palmer, who left Renault last year after two seasons in Formula One, believes those types of clashes actually prove how much respect there is between them.
“What they’ve got is a lot of respect between them,” Palmer said on BBC Radio 5 Live.
“They’ve both won world titles, in dominant cars it has to be said, and in almost different eras with the Red Bull V8 era where Vettel was so strong and now Hamilton at the moment.
“They are vying against each other directly. They’re in the two title fighting teams – Mercedes and Ferrari – they’re both on four titles and there is respect.
“It’s not respect on the track, it’s in the heat of battle but in a way it’s respect in as much as they’re showing no respect but they know that they are the two guys fighting for the title.
“Vettel and Hamilton were head-to-head at the front of a race and the fact that he was getting so infuriated by what Hamilton was doing and the ding-dong between them shows how much the other one means to each other because it’s the two of them going head-to-head.”
