The Cape Verde international has been the subject of two Newcastle bids.
Newcastle have already made two approaches for the Cape Verde international. Turkish Football claim that Galatasaray rejected a £6 million bid from the Tyneside giants in August. A report from Gunes recently stated that Newcastle saw a second offer for Rodrigues turned down once again in January.
The Turkish giants have landed themselves in some financial difficulty and are therefore looking to move on some big names in the summer.
It is claimed a bid of €10 million (£8.8 million) would be enough to secure his services - so Newcastle are not far off with their most recent offers.
Rodrigues has been in fine form for the Istanbul side this season. Rodrigues, who can play on either flank, has set up six goals in 16 league starts. That form therefore means Newcastle are not alone in having an interest in signing the player.
The report claims Real Betis, Celta Vigo and Schalke 04 are also keen on his signing.
Newcastle will hope to remain in the Premier League, so they can convince Rodrigues to head to the UK this summer.