The Telegraph says City manager Pep Guardiola and his side will target a new striker, left back and a defensive midfielder in their mega-money overhaul of their squad.
One area of concern is a long-term replacement for striker Sergio Aguero who has struggled with injury problems since the start of the season.
The Argentinian striker is City's all-time record goalscorer but the 32-year-old striker's contract expires in six months with Aguero yet to make a decision on his future.
But City will reportedly target a new striker even if Aguero ends up staying at the Etihad beyond this summer.
Lukaku left Manchester United last year for Inter and hasn't looked back, scoring 51 goals in 73 matches for the Nerazzurri.