The 30-year-old is reportedly unhappy at Craven Cottage and is seeking a move away from London.
Kean has confessed that Johnson is just one of a number of targets that Rovers are currently pursuing.
"We respect Fulham and we don't want to disclose what level that's at. That will remain private between the two clubs. That's one name," Kean told Sky Sports News.
"There are another four or five names we're actively trying to pursue. As you know you can have the biggest list in the world, but when you knock on the door of another club and you ask if they're available sometimes they say no.
"And you've got to respect that and move on."
Johnson joined the Whites in 2008 from Everton.