Walcott finalised a £20m move from Arsenal on Wednesday, following in the footsteps of Tosun who arrived form Besiktas for £27m earlier in the window,
The German-born striker is excited by the chance to link up with the former Southampton winger, describing him as a "massive signing".
"Theo is a great player," Tosun said. "He's a proven player and has done well for Arsenal for many years. I would say it'd be a massive signing for us.
"I think I would link up well with him. We already have very talented players in our team and I'm sure if we sign him he would have a great input."
Meanwhile, the Turkish international also explained how manager Sam Allardyce played a big role in bringing him to Merseyside.
"Everton is a massive club. Sam Allardyce played a big role in this, the club wanted me a lot I felt that," he explained.
"To play in England is one of my biggest dreams. Our supporters are a great bunch, and it's a massive club with a big history."
Tosun made his debut in the defeat to Tottenham at the weekend rubbished suggestions that his price tag could put pressure on him, saying that he felt honoured to be valued to highly.
"It doesn't put a lot of pressure on me to be honest, it's actually a great honour," said the 26-year-old. "I would like to become a good role model to the other players in Turkey.
"There are some great players in Turkey but it's difficult to make the breakthrough so I would like to open the door for them."