According to Turkish media, coach Mehmet Altiparmak confirmed the deal, saying everything will be finalized in a few days.
Erzurumspor is a newly-promoted SuperLig club and has been attracted to the Bafana Bafana winger.
Reports suggest that Shabba has been offered him a two-year deal.
Although the Soweto giants are yet to confirm or announce the proposed deal, it looks like coach Giovanni Solinas will be without Tshabalala for the remainder of the season.
"With Siphiwe Tshabalala, we have a principle agreement. We will complete this transfer within a few days," Altiparmak was quoted as saying by Turkish media.
Meanwhile, the club has signed the likes of Khama Billiat and Lebogang Manyama to bolster their attacking options, and Tshabalala's departure may not hurt the Soweto giants regarding their aspirations to lift a number of trophies in the current PSL season.
On the other hand, 'Shabba' could play his final match for the Soweto giants should coach Solinas decide to use him this weekend against SuperSport United in the MTN8 Cup semi-finals.
Tshabalala's agent Jazzman Mahlakgane was not available to share an update on the transfer as his phone rang unanswered on Friday despite initially promising to gather more information on the reports.
The 33-year-old has represented Amakhosi in over 300 matches in all competitons and has won the PSL, MTN8 Cup, Telkom Knockout Cup as well as the Nedbank Cup titles during his 11-year spell with the Naturena-based side.