Well Mike is a full fledged retard by the time BB rolls out so why would he not blurt things to Saul? He loses all of his money because of incompetence. And then gets owned by Walt a dozen times. Mike uses plastic zip ties to hold Walt hostage instead of having someone watch Walt, letting Walt easily escape. Then like a total buffoon has Walt pick up a bag with a gun in it that Walt uses to waste him. Mike's told by Nacho to kill Tuco. Mike cooks up the braindead plan of letting Tuco nearly beat him to death, get arrested for a gun charge (which fails), and then causes the Salamancas to threaten his entire family completely exposing him to the cartel. He tells Nacho that sniping Tuco is high risk. Yet a week later his granddaughter has cartel assassins pointing guns at her.
Mike is literally one of the dumbest characters in all of BCS and BB. Almost everything he does winds up failing in the short and long term. For all his master assassin writing he is basically a dolt at everything else. So I doubt that he would keep a secret from Saul if Saul asked because the question would almost be rhetorical at that point. "Hey Mike have you heard from Nacho or Lalo lately?". Any answer would tip off the truth.