Tigers come to Northampton on the crest of a wave, having won all six of their Gallagher Premiership games so far this season.
But Saints are also full of belief after thrashing Worcester Warriors 66-10 at the Gardens last Friday. It was a fourth win in five league matches this season for Chris Boyd’s side.
And they are now set for their toughest test of the campaign to date, against their reinvigorated rivals from Welford Road.
“Leicester know exactly what they’re trying to do and they all buy into it and do it really well,” said Leicester-born Vesty, who made 164 appearances as a utility back for Tigers during his playing days.
“They’re all swimming in the same direction now and their game is based on putting the other team under pressure with kicks and kick-chase and they do it really well, with a boat-load of enthusiasm.
“When they do get the ball, they rely on a power game, and they’ve got the athletes to do it.
“Ultimately, they will want to come and bully us - and good luck to them!”
Both teams will be without their England players this weekend, with Saints losing Courtney Lawes, Lewis Ludlam, Tommy Freeman and George Furbank to this week’s Monday-to-Friday training camp in Jersey.
Tigers are without five men due to that, with Ellis Genge, Nic Dolly, George Martin, Ben Youngs and Freddie Steward all away.
And Vesty said: “It seems sad that some of the biggest games in the Prem are played while some of the best players are away.
“It’s a tricky, difficult situation with the club v country debate but you’d like to think there was a solution so that the players could play in the biggest club games.”