The 32-year-old looks set to leave St James’ Park after a three-year stay on Tyneside when his contract expires in the summer.
And according to the report, both Palace and West Ham have made an offer for the midfielder for next season.
Turkish giants Fenerbahce are also thought to be interested in securing the services of the Senegal international.
Diame has plied his trade in England for the past 10 years, turning out for the likes of Wigan Atheltic, Hull City and West Ham prior to his time with the Magpies.
Palace boss Roy Hodgson is thought to be keen on bolstering his midfield options this summer, so securing the services of Diame for no transfer fee could prove to be a smart piece of business by the Eagles.
Four more Premier League midfielders Palace could target this summer
Jean Michael Seri
Seri looks set to be offloaded by Fulham following their relegation and could be a realistic option for Palace.
Liverpool midfielder Grujic has endured a frustarting stay at Anfield and may well be open to a move to Selhurst Park next season.
Palace could face plenty of competition for Cardiff’s Camarasa this summer following his impressive individual campaign.
Huddersfield midfielder Mooy could also be of interest to multiple Premier League sides following the Terriers’ relegation.