The 20-year-old is yet to feature for Hull since signing from Cork City in August, having caught the eye playing in Ireland's top flight.
Coleman has not featured for Everton since their 4-1 UEFA Europa League win over Wolfsburg on September 18.
The full-back took a blow to the head in the game against the Germans, and O'Neill is not confident he will recover in time for Saturday's Euro 2016 qualifier against Gibraltar, and is also expecting Coleman's club-mate James McCarthy to be absent.
O'Neill said: "We are going to bring up young Brian Lenihan at Hull because we don't have any natural right-back in the team at the moment, so he will come in later on today and train with us tomorrow.
"I was speaking to some of the lads here at Hull, who said he has settled in well, and of course he is delighted to be coming.
"I haven't spoken to [Everton manager] Roberto Martinez, but I had a word with Seamus - Seamus doesn't feel fantastic at the moment.
"There was talk about James being available, or trying to be available, for last Sunday's game against Manchester United, but I think that was a long shot.
"At the moment, you would say that there is no chance of them being available."
O'Neill also revealed that veteran goalkeeper Shay Given is struggling with a hip injury.
