The Süper Lig outfit have requested for negotiations to go ahead with the 31-year-old striker who is currently a free agent after being released by West Ham.
Cole first joined the Hammers in 2006 and scored a total of 57 goals in 259 appearances in all competitions for the Premier League club.
The experienced striker has also been linked with Leicester City. The Foxes boss Claudio Ranieri is reportedly considering a move for Cole according to the Mirror.
Ranieri knows Cole all too well from his time in charge at Chelsea. The Italian coach gave Cole his debut as a teenager in 2002 and reportedly gave him the nickname Tyson due to his size and strength.
Sivasspor are currently managed by Sergen Yalçın and will play at the brand new 29,000 capacity Sivas Arena starting from next season. The Yiğidolar finished last season in 12th place on 38 points.