The defender has not featured for Rovers since his sending off against Arsenal in February, having fallen behind Grant Hanley and Scott Dann in the pecking order. And he was not even named on the bench despite travelling with the squad as the Lancashire club slipped deeper into the relegation mire with an abject display at the Liberty Stadium.
Kean stopped short of saying Givet had refused to play, but he said: "It was apparent when I spoke to Gael this morning he wasn't anywhere near in the right frame of mind to play today, whether starting or on the bench. I will speak to him again, and if he is in a better frame of mind then great, but he was nowhere near in the right frame of mind today."
He added: "I can't get inside somebody's head, I can only say how much we and his team-mates need him.
"If you look at David Dunn with his hamstring, he is having injections to play. We need guys who want to play even if they are injured or their heads are not quite right, but I would rather keep the conversation between myself and Gael private."
Gylfi Sigurdsson's seventh goal for Swansea, his first at the Liberty Stadium, opened the scoring with Nathan Dyer and a Dann own goal completed a comprehensive win.
And manager Brendan Rodgers praised the way his players had responded after the 3-0 defeat at QPR in midweek, and revealed a team meeting on Thursday had laid the foundations for a return to winning ways.
He said: "I felt I needed to reframe the players' minds. We had a team meeting and I wanted to take the anxiety out of them. I felt we were a little anxious on Wednesday and I wanted to frame their mindset and remind them how they have played all season.
"We talked about how we felt in that game because it was certainly different to what we had been used to seeing up to a month ago.
"I wanted to tell them how brilliant we had been. There had been a couple of doubters in recent weeks but that's modern life. I felt it was important to make sure that we knew how to control any distractions and cut out any negativity."
Source: PA
Source: PA