Mbappe finished this World Cup with 10 goals, two more than Messi in the race for the Golden Boot, which is awarded to the tournament's top scorer. Should he remain ahead of Messi after Argentina play Spain in Sunday's (5am Monday AEST) final, he would become the first player to win the Golden Boot twice.
"It's for sure that when you score that many goals in the World Cup, it elevates you to certain levels, but I would have liked to not be the top scorer in history and play tomorrow's (championship) match," Mbappe said after the fight for bronze.
"So, I think it's good for legacy and when we stop (playing) to say that I was one of those players. But today, it's not the first thing crossing my mind."
France trailed England 4-0 when Mbappe flicked a shot past goalkeeper Dean Henderson in the 48th minute. Then he beat Henderson again with a left-footed strike from about 14 yards in the 66th minute to pass Messi's career mark of 21 goals.
France pulled within 4-3 on Mbappe's second goal. Les Bleus missed out on a chance at playing in their third straight World Cup final when they lost to Spain in the semi-finals.
The Real Madrid striker scored eight goals to win the Golden Boot four years ago in Qatar, where France lost to Messi and Argentina in a penalty shootout in the final.
Mbappe started the match, and his quest for the Golden Boot appeared to be going nowhere when France trailed 4-0 at halftime. England stars Harry Kane and Jude Bellingham were not in their squad's starting line-up, although Bellingham entered as a substitute and scored late in second-half added time. He finished the tournament with seven goals, one more than Kane.
WORLD CUP ALL-TIME TOP SCORERS:
* 22 - Kylian Mbappe (France)
* 21 - Lionel Messi (Argentina)
* 16 - Miroslav Klose (Germany)
* 15 - Ronaldo (Brazil)
* 14 - Gerd Muller (West Germany)
MBAPPE'S WORLD CUP GOALS FOR FRANCE:
* 1 v Peru (Yekaterinburg, 2018)
* 2 v Argentina (Kazan, 2018)
* 1 v Croatia (Moscow, 2018)
* 1 v Australia (Al Wakrah, 2022)
* 2 v Denmark (Doha, 2022)
* 2 v Poland (Doha, 2022)
* 3 v Argentina (Lusail, 2022)
* 2 v Senegal (East Rutherford, 2026)
* 2 v Iraq (Philadelphia, 2026)
* 2 v Sweden (East Rutherford, 2026)
* 1 v Paraguay (Philadelphia, 2026)
* 1 v Morocco (Foxborough, 2026)
* 2 v England (Miami Gardens, 2026)
With Reuters.