The Belgian striker has already scored two goals in pre-season friendlies for his new club and impressed against La Liga giants Real on Sunday evening.
After the victory in Santa Clara, Lukaku was spotted in conversation with Bale and the Wales international has revealed what was said between the pair.
‘I just wished him good luck for the season,’ Bale, 28, said. ‘He has just signed for them and I hope he has a great season.
Man Utd's pre-season fixtures
Man Utd 5-2 LA Galaxy
Man Utd 2-1 Real Salt Lake
Man Utd 2-0 Manchester City
Man Utd 1-1 Real Madrid (2-1 on penalties)
Barcelona – Wed 26 July
Valerenga – Sun 30 July
Sampdoria – Wed 2 Aug
Real Madrid (UEFA Super Cup) – Tue 8 Aug
‘I’m sure he knows all about the spotlight [from his time at Everton and Chelsea]. He has been playing for long enough now.
‘He has done very well in the Premier League and I am sure he will do great for them.’
Lukaku opted to join Jose Mourinho’s Red Devils earlier in the month despite attracting substantial interest from Premier League champions Chelsea.
Antonio Conte was keen to bring the 24-year-old to Stamford Bridge but was forced to turn his attentions to Alvaro Morata after Lukaku put pen to paper at United.
Speaking to Metro.co.uk, legendary striker Michael Owen backed Lukaku to justify his hefty price-tag and score at least 20 goals a season at the Theatre of Dreams.
‘I don’t really see how he can’t be a success,’ the 37-year-old former United, Liverpool and England star said.
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‘He’ll be playing in a team that will create a lot of chances and he’s a top player so it’s inevitable he’s going to score goals.
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‘The only question is how good can he be? Could he become a top United player for years to come?
‘I fully expect him to score more than 20 goals a season so it’s just a matter of how well he can do.’