Manager Phil Brown revealed on Tuesday morning the club had agreed a fee with West Ham for Boa Morte while they had also been given permission by Wigan to speak to Kilbane.
Both players would offer balance on the left of Hull's midfield and Brown hopes they will also freshen up his squad after a run of just one win in 12 Premier League matches.
Brown, whose side face Newcastle in an FA Cup third-round replay tomorrow, said: "The clubs have agreed terms on Luis Boa Morte and we are trying to agree terms on Kevin Kilbane, on a personal front as well.
"There is no real rush at the moment, we are concentrating on the Newcastle game but hopefully Thursday or Friday there will be some movement.
"We have made reference to talking to both players and if they both come then fantastic.''
Former Portugal international Boa Morte, 31, has struggled to earn a regular starting slot at Upton Park since a £5million move from Fulham in summer 2007.
Republic of Ireland winger Kilbane, also 31, is thought to be ready to move on after falling down the pecking order at the JJB Stadium.
Brown does not intend his January recruitment to end there with plans also being made to find a striker and a defender.
He added: "We are down the line on a number of them but these things are a slow process. We have got another couple of weeks to work at it and hopefully bring the right players in to improve the squad and bolster the confidence levels.
"To freshen the place up wouldn't be a bad thing.''
Brown is likely to rotate his squad at St James' Park but still recognises the importance of a victory.
Hull briefly went joint top of the table in October but their form since has left them looking over their shoulders with just seven points separating them from the bottom three.
Brown said: "The atmosphere is not too bad around the camp but what a win would do is lift spirits, raise confidence levels and get back to the level of performance we were at towards the beginning of the season.
"We are looking forward to the game. We have got a fair-sized squad so we will be making changes, but we will be going in there with the mentality we can win and then we will hopefully take that confidence into our league form.''
Brown concedes opponents have now got wise to Hull's players and style but he is loving the challenge of competing in the top flight.
He said: "I don't think it has gone wrong but when we arrived in the Premier League we were an unknown quantity.
"After seven, eight, nine games eyebrows were starting to be raised at the performance levels and the results Hull City were getting.
"Everyone has battened down the hatches, is paying us the respect we deserve and bringing their best games to the table.
"But we are trying to concentrate on the fact we have won games at this level and we need to start winning games at this level again. A confidence-boosting performance at Newcastle might stand us in good stead for our league form.
"I know my players are looking forward to the challenge ahead and with the addition of one or two, hopefully we will succeed in that challenge.''
Hull have managed just two goals in their last five outings but Brown is hoping luck changes soon.
"It would be a concern if we weren't creating chances,'' he said.