The Gabon international’s contract ends this summer and is yet to sign a new deal with the Championship side.
BBC Wales Sport has learned that Manga has attracted interest from Turkish club Bursaspor.
There is now more optimism at the club that the 28-year-old may choose to remain in the Welsh capital despite being offered a deal on reduced terms.
Manga joined Cardiff from French club L’Orient in September 2014 for a fee of almost £5m.
Though he has had his fitness problems – including a bout of malaria – while at Cardiff, he has been a defensive mainstay.
It had been thought that after being asked to take a pay cut Manga would most likely choose to leave Cardiff.
Indeed Bluebirds’ boss, Neil Warnock, admitted recently he already had a replacement lined up for Manga.
But after further talks in the last few days, there is now more optimism he will stay with negotiations set to continue this week.
If Manga remains, he would provide a major boost to manager Neil Warnock as he revamps his Championship squad for next season.
On Friday, Cardiff announced striker Kenneth Zohore had agreed a new dealwith the Bluebirds to remain with the club until 2020.
Stalwart midfielder Peter Whittingham is still mulling over his options having also been asked to take a pay cut to stay.