Ivanovic has fallen out of favour at Chelsea since Conte was appointed as manager last summer.
Despite boasting years of experience, the Serbia international could leave Stamford Bridge this month.
Russian giants Zenit St Petersburg are interested in ending his nine-year stint in London.
Branislav Ivanovic could leave Chelsea this month
In-demand Chelsea duo train ahead of the Blues' FA Cup clash with Brentford
Fri, January 27, 2017
Asmir Begovic and Branislav Ivanovic were both in Chelsea training today despite potential moves away from Stamford Bridge in the next few days
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Chelsea train ahead of their FA Cup Fourth Round clash with Brentford
Branislav Ivanovic has won the title twice at Chelsea
And Conte has admitted he is unsure where Ivanovic’s future lies.
“I don’t know,” he said when asked about Ivanovic’s future.
“This month has this window and there is a lot of speculation – a lot of lies and lot of truths in some situations.
Antonio Conte is unsure on Branislav Ivanovic's future
“There are four days to finish this window and then we see this situation. I don’t what will happen at the end of this window. The club knows my thoughts.”
Ivanovic is the Blues’ second longest-serving player behind John Terry.
The 32-year-old has won two Premier League titles since joining from Lokomotiv Moscow in 2008, as well as the Champions League in 2012 and Europa League in 2013.