The Wolves defender has attracted the interest of the Toffees during the summer transfer window.
Coady, 29, is captain at Molineux, having been at the club for the past seven years, and played in every Premier League game last season.
But the former Liverpool centre-back’s future is now uncertain as Wolves plan to switch from back five to a four-man defence for the upcoming season.
He was omitted from several pre-season matches.
Lage has the utmost respect for Coady but did not rule out him leaving the midlands outfit.
Coady is keen to retain a spot in the England squad ahead of the World Cup later this year.
What’s been said
The Wolves boss (h/t Express & Star) said: “He’s one of the best people I know in football. I had a great season with him and I think he had a great season with me.
“Today, I can say he is a guy that I will keep in my friendship because he is a lovely guy. He is my captain, he still is my captain.
“Since Wolves arrived in the Premier League, they played 152 games. Coady played 151. He played all games with me. He didn’t play one game in 2020 against Southampton because I think he was in touch with someone with Covid-19.
“Massive respect from me to Coady, massive respect from the club. I need to take my decisions.
“Sometimes I play with two midfielders, three midfielders, with four midfielders. Now I have more solutions and will make the best decision for my team but I cannot forget Coady or any player.
“It’s not just about the World Cup, every player wants to play. Coady and all the players are focused and try to improve in a line of four. I have all my team motivated.
“I really don’t know (if he will leave). But I will respect him and understand what is best for him. You don’t know how we will play tomorrow, a five or a four.”