Taylor wanted to bring in an experienced midfielder to add to his large squad, but ended up signing Junior Lewis instead.
He told the Hull Daily Mail: "I did consider signing him two or three weeks ago because I wanted an old head in midfield.
"He has got a lot of experience and is a good professional. In the end though I made an enquiry for Junior Lewis at about the same time, suddenly I was told he was available so I signed him."
Groves was sacked as player-manager of the Mariners after a humiliating defeat at Oldham, immediately prompting speculation linking him with a move to Scunthorpe to team up again with Brian Laws - who managed him previously at Grimsby.