Lukaku is likely to be the replacement for Ibrahimovic, who after a stellar 2016/17 season at United, was released after his contract expired on 30 June. The former PSG man scored 17 league goals in 28 games last season.
Neville believes Lukaku, who scored 25 league goals for The Toffees in 2016/17, is a different type of player whose speed will benefit United and give them plenty of options.
"I think you've seen an improvement, I think there were of couple of criticisms. Can he play in big games? Can he score in the big games? I think he half-dispelled that last season," Neville told BBC Radio Five Live, as quoted by FourFourTwo.
"He scored in a couple of the big games and I think he is improving all the time. I think he's a different type of striker from what United have had for a long time, someone that can probably run in behind, can be a little bit of a battering ram, that United can play on the counter-attack.
"I think with Zlatan last season, United couldn't play on the counter-attack because obviously his age and the fact his legs are slowing down a little bit. Now you've got someone with genuine, genuine speed that United can play on the counter-attack."
Neville, who played for both United and Everton, also heaped praise on the Belgian international's knack for goals, claiming that anything between 17 to 20 goals and above would represent a successful debut season at Old Trafford.
"It will be interesting to see how he fits into this United team because there's a lot of talk about 'Jose sold him, didn't play him at Chelsea', but that was four or five years ago," he added. "Romelu Lukaku is a different player now, he is a better player."
"His record actually is sensational. I mean 25 goals last year, 18 the year before. If you go back to his West Brom days when he was on loan there from Chelsea, [he scored] 17 Premier League goals. If he gets anything like 17 to 20 this year, United will be successful."