Davids' representative Robert Geerlings suggested over the weekend the 36-year-old, who is a free agent, would be interested in returning to England with Leicester.
"There has been interest but whether anything materialises is neither here nor there at the moment because there is still a long way to go if anything does happen," Pearson told Leicester's official website.
"As with all our signings we have made or targets we look at, they have to meet certain criteria and this one will be no different. I don't believe in publicity stunts and I don't believe in players coming in who don't meet that criteria.
"I can understand there being interest in this and things can move quickly in football but it would be wrong for me to speculate further until there comes a time when there is something more concrete to talk about."