Arsenal remain in the market for a full-back with their move for Kieran Tierney still shrouded in doubt.
Alves is a free agent after leaving PSG this summer and has a cluster of clubs monitoring his situation.
One of those is Italian side Inter Milan and they look most likely to provide the Gunners with competition, according to Goal.
Inter’s Serie A rivals Juventus are also thought to be considering offering the 36-year-old another spell in Turin.
Alves has teased on Instagram about his availability questioning whether any potential suitors have the time to consider him.
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“Looking for a job, where do I put my resume?” he said.
“Someone let me know if you have time to read!”
Arsenal fans will be hoping Unai Emery finds the time to browse the right-back’s CV before their season opener against Newcastle.
That should be made easier now that the Spaniard has sealed deals for William Saliba and Dani Ceballos.
The latter has joined on loan from Real Madrid which suits Arsenal’s minimal transfer budget and Alves’ availability on a free should attract Emery.
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Especially with the potential transfer fee they are set to pay Lille for Nicolas Pepe, although any deal is likely to be done in instalments to suit the north Londoners.
An addition at full-back though remains on Emery’s list as he attempts to plug the gaps in his Arsenal side.
Alves has won 40 major honours across a career that has featured stints at Barcelona, Juventus and PSG.
He is fresh off winning the Copa America with Brazil, but that success hasn’t helped him secure a club with the season nearing.