The 27-year-old forward has expressed his desire to leave Manchester City to be nearer to his family, and a big money move to Brazilian side Corinthians looked likely until it fell through this week.
Walker believes that the prolific forward could remain in the Premier League despite claiming he wants to move back to South America.
“When we first saw this about Tevez wanting to go back to his family and play in South America, it seemed a little bit bizarre to me,” Walker told talkSPORT.
“If it all unfolds and he ends up moving to London or Europe, it would show how cut-throat players are today. They see a move, they want a move, they want more money and that would be him.
“But I wouldn’t be surprised if that happened because this is how it seems to be turning out with players these days.”
Walker speculated that there could be a place for Tevez at Stamford Bridge if the former Premier League champions are interested.
“I can see him moving to a big club, of course, because there are only a few clubs who can afford and, if Chelsea are in the market, I am sure they can afford him," he added.
Manchester City are reportedly ready to make a bid for Atletico Madrid star Sergio Aguero, however the move is not dependent on the situation of Tevez.