The English Premier League side were tracking the 22-year-old during the January window but were unable to complete a transfer after Lille refused to cash in.
Reports say Lille rejected at least one offer from the Gunners, who failed to meet the valuation, while fellow Premier League side Everton also saw a bid knocked back.
That will not be the end of the matter and Arsenal, who are keen to bolster their defensive options, will test Lille's resolve once again, and may even match the asking price to try and get a deal over the line.
It is also claimed Lille have tied the player down to a new deal stretching until 2023, which will put them in a strong position regarding any future transfer fee.
They will be under no pressure to sell and can demand big money before agreeing to a transfer.
Gabriel is not the only Lille player wanted in England either as reports claim Chelsea are tracking goalkeeper Mike Maignan.
The 24-year-old is highly rated by Lille and, following some fine performances in Ligue 1, he has caught the eye of the Blues, who are looking to replace Kepa Arrizabalaga.
Lille paid Paris Saint-Germain just £1million for the goalkeeper back in 2015 and will make a huge profit if they decide to cash in during the summer.