Walker was the first-choice option on the right-hand side of the defence for both Spurs and England before departing for Manchester City, where he won the Premier League title last season.
But the City man formed part of a central back three in Russia as Trippier took up his preferred wing-back role, impressing and netting in the semi-final defeat to Croatia.
Trippier does not consider himself to be better than Walker, though, ranking the 28-year-old as the world's best.
"At this moment in time, for me, personally, Walks [is the best]," he told Sky Sports.
"When I was playing with him at the World Cup, [you could see] how quick and powerful he is. Even on the ball, you see it at Man City, he's so comfortable.
"He's got everything for a full-back, and he's only getting better playing at Man City. So for me, he's the number one right-back in the world."
Trippier and Tottenham finished third in the Premier League last season and, although the club did not bring in any new signings, the England defender is confident for the new campaign.
"It doesn't matter [about signings]. We know the squad we've got," he said. "We've got the manager, the players, and we've got so much quality in this team.
"We've got depth as well, so many good players waiting to play. Not signing a player? That doesn't play on our minds, we've just got to fully focus on what's ahead of us."