Soon after the end of the campaign, Lemina revealed that he was flattered by alleged interest shown in his signature by Arsenal and Watford.
The Hornets appear to have turned their attentions elsewhere but according to Italian journalist Tancredi Palmeri, Arsenal are pressing on with their bid to take the 23-year-old to the Emirates Stadium.
It has been claimed that negotiations between the two clubs are already underway with Arsenal likely to be able to offer Lemina more first-team football over the coming years.
He has made just 15 Serie A starts in two years in Turin and with Juventus having been linked with both Steven N'Zonzi and Andre Gomes, it appears that they are looking to strengthen in the centre of midfield.
At times last season, Arsenal were criticised for their lack of steel and Lemina would be able to improve that aspect of their play should Arsene Wenger be able to complete a deal for his services.