The Portuguese international joined the Scottish club from Cagliari in Italy at the beginning of last season, and went on to play 25 times for the club.
However, with the 36 year-old on the verge of a return to Serie A with Parma, Steven Gerrard is looking to find a replacement in defence.
It seems as though Jake Cooper from Milwall is one of the potential players that could fill the gap left by Alves. The player joined his current club from Reading in 2017, and went on to make 39 appearances in all competitions last season for 'The Lions'.
Gerrard has already spent £5 million on bringing centre-halves to Ibrox, as the former Liverpool captain looks to re-build the squad to try and challenge Glasgow rivals Celtic for the Scottish title next season.
The club first face qualifying matches in the Europa League before they get their Scottish Premiership campaign under way away at Aberdeen on 5th August.