The 17-year-old has been given a pricetag of £20 million and his agent has confirmed there is interest from a host of top clubs.
Belgium international Lukaku was top scorer in the Belgian First Division last season, scoring 15 times in 33 appearances.
The 6ft 3" forward is contracted with Anderlecht until 2012, but the club could be tempted to part with their star if a big-money offer arrives in the January window.
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The Daily Mail reports Manchester City are planning another crack at signing Wolfsburg striker Edin Dzeko.
Roberto Mancini was in for the 24-year-old over the summer, but City failed to meet Wolfburg's £40m valuation.
If that one doesn't work out, Mancini continues to monitor the Fernando Torres situation and is reportedly not averse to bringing Zlatan Ibrahivomic to Eastlands.