He wasn't even on the bench for the next game against Yeovil, officially because of a 'dead leg' but rumours suggest off-the-field factors led to him being excluded.
The 32-year-old was then shipped out on loan to Sheffield United where he has yet to concede in 1½ games.
Following yesterday's signing of Boaz Myhill from Aston Villa, Fettis has been placed on the transfer list.
Taylor said: "Alan knows the situation. He's told me he wants to be a number 1 but that's something I can't offer him. We've talked things through and we will be listing him."
The Belfast-born keeper has played 23 times since signing from York on a free transfer in January. In addition to his first spell at the club in 1991-96, his overall total appearances in a Hull City shirt stands at 178 in all competitions - and includes two goals scored during a brief spell as a makeshift striker.