Brazilian playmaker Willian is one of the hottest properties in football and has been linked with moves to both Chelsea and Tottenham in recent months.
However, Eduardo, who spent three years with Arsenal, believes Spurs are not good enough for the 24-year-old.
"There are three clubs who are big enough and good enough for Willian - Arsenal, Man United and Chelsea," he said.
"I have recommended these clubs - no others. He needs to play at one of the best teams.
"Willian is a complete player now. He is ready to play for a big club and become a really big player.
"He should play at a top, top club because he is a class player. He can play in England, for sure.
"We always talk and watch Premier League games together.
"He asks me about England and the English game and I tell him little things."
Shakhtar travel to London to take on Chelsea in the Champions League on Wednesday and Eduardo admits scoring at Stamford Bridge would be extra special.
"I am a Shakhtar player and an Arsenal fan," he added. "I know if I score against Chelsea the Arsenal fans will be very pleased."