Instead, the Welshman believes that several of Lukaku's team-mates need to up their game ahead of the new Premier League season.
Speaking to 'The Telegraph', Giggs said: "The main reason Jose bought Lukaku is for goals and to turn all those draws at Old Trafford into wins."
"There will be a lot of pressure and scrutiny on him but those around him also need to step up and score more."
"Juan Mata did his fair share, but [Anthony] Martial, Marcus [Rashford] and [Henrikh] Mkhitaryan have got to get double figures. So although the most pressure will be on Lukaku, the onus is on the whole team."
It seems strange that Giggs would praise Mata but criticise Rashford given that the youngster actually scored more goals in all compeitions than the Spaniard last season, albeit after featuring in more games.
Lukaku has big shoes to fill following Zlatan Ibrahimovic's goalscoring exploits last season but has started his United career well with 2 goals in 2 friendly games.