The 26-year-old, whose side face Rochdale in the last 16 of the competition on Sunday, said that it was a "dream" of his to play in the FA Cup while watching the competition in Kenya's capital, Nairobi.
The midfielder, speaking to The Telegraph, added that his side are confident of lifting the trophy this term.
"The FA Cup was a big thing at home," Wanyama said. "Only the semi-final and then the final were shown on television in Nairobi, so it was a big thing to watch. The last final I remember watching there was Manchester United against Chelsea [in 2007], when Chelsea won. It's a big deal, a big trophy to win.
"Back then, it was only a dream for me to play in the Cup and also in England. Now I have a chance and it would be a good thing to arrive in the final and maybe even win it.
"We have a very good group of players and we always want to win everything. We believe we can compete with anyone and win."