"In the winter I got a call from Tottenham," he told Championat.com.
"There was a very tempting loan offer until the summer, for 3-4 months. It seemed attractive to me. Why not try it? Kane broke down and it really was a chance.
"I was culturally told that this is impossible. 'Focus on Zenith,' I heard."
Dzyuba added: "Specifically, another option was discussed with Crystal Palace. But I don't know all the details."
The Russian also had offers last year from England.
"I didn't give up Cardiff . There was no such thing that I was asked: 'Will you go there or not?' and I said no. There was talk about a choice of three clubs. I was told that West Ham coach (Manuel) Pellegrini was personally interested in my services.
"So I ended up saying, 'If I choose between West Ham and Cardiff, I'm certainly for West Ham'."