Lukaku has been linked with a move to Inter for much of the summer and has already agreed personal terms with Inter.
But Inter’s desire to spread the transfer payments over three years have been rejected by Manchester United, who are looking for upwards of £80m for the striker.
Lukaku hinted an end to the saga would come this week after claiming news would develop following United’s clash with Perth Glory on Saturday
Asked about his future as he left the Optus Stadium following United’s win in their first pre-season tour game, Lukaku told reporters:
‘You guys will know something next week.’
Lukaku was left out of the United squad that defeated Leeds United 4-0 on Wednesday.
According to Tuttosport and Corriere dello Sport, Inter have started to look for alternatives to Lukaku and one name being mentioned is Paris Saint-Germain striker Edinson Cavani.
The former Napoli hitman is viewed as a cheaper option, given he is 32 and has only one year left on his PSG contract.
Cavani is a proven goalscorer, having scored 193 goals in 279 games for PSG, winning five Ligue 1 titles.He netted more than 100 times for Napoli between 2010 and 2013 before his €64m transfer to PSG.