Keane says the Black Cats have agreed personal terms with three of the four Tottenham players he is trying to sign – Steed Malbranque, Younes Kaboul, Pascal Chimbonda and Teemu Tainio.
The Sunderland boss expects a conclusion to his pursuit of the
Spurs quartet by the weekend, but that does not mean everything is signed, sealed and delivered yet.
Despite Kaboul's agent saying the French under-21 captain was extremely impressed with Sunderland, their manager and facilities, Portsmouth boss Harry Redknapp claimed yesterday the centre-back wants to join Aston Villa.
Keane is trying to steer clear of such rumours – putting his faith in the work being done by chairman Niall Quinn and chief executive Peter Walker – but acknowledges his hunger to introduce new recruits.
He said: "I wouldn't get bogged down with deals being done by today or tomorrow, but I certainly hope they will be by the weekend.
"There is progress being made, but you know the score.
"You are dealing with clubs and sometimes the players have disagreements with the clubs they're leaving.
"One or two of the issues we're facing are basically out of our hands. It's between the players and Tottenham.
"On personal terms, we're virtually there with three of them, if not four, but there are one or two loose ends to be tied up.
"I have been in the game long enough to know that things can drag on a little bit but in defence of Peter and Niall I'm not disappointed at all (with the work going on behind the scenes) because we really are going full steam ahead.
"Agreeing the price with a club is just the start of it.
"Trust me, I know everyone's impatient for news, particularly the Sunderland fans, but if you want to meet an impatient person then I'm one.
"But I've also got to understand that hopefully it will be worthwhile because they're quality players."
Keane would not reveal that names of other players he is interested in, but was asked in Portugal if he is in for another Spur, Darren Bent.
He said: "I don't think it's fair to talk about other clubs' players when fees haven't been agreed.
"We got permission to talk to the four Tottenham lads and the talks went as well as I hoped.
"It was nice to meet the players. We had one or two examples last year when we never even got that opportunity.
"Having agreed fees with clubs, players refused to even travel up, which I thought was unbelievably disrespectful to the football club.
"The four Tottenham lads were very keen to come up and listen to what I had to say.
"It would be nice to get a few medicals done in the next few days – we're certainly on standby to do that.
"There are one or two other things going on – shall we say discussion over fees – and that will probably go on for another two or three days.
"In terms of the four Tottenham lads, we should know one way or the other by the weekend, but in terms of the two or three other deals we're looking at, we might have to be patient and wait for the next week."
The injury difficulties of last season, when Keane was without the likes of Carlos Edwards, Kieran Richardson, Dean Whitehead, Ross Wallace and Danny Higginbotham for lengthy periods, have reinforced the need to bring in more players.
Keane added: "If you look at the problems we had last year, losing Carlos, Deano and Kieran, we were up against it right from the start.
"We don't want to be in that situation again - we need a bigger stronger squad."
Kaboul's agent Rudy Raba says he will decide over his situation soon.
Raba had previously insisted the defender would not sign for the Black Cats.
But he backtracked yesterday, saying: "Younes was very impressed with Roy Keane when he met him, especially with his vision for Sunderland Football Club.
"He was also very impressed with the city, stadium and facilities which, to be fair, are second to none.
"Younes also appreciated the fact that Roy and Sunderland have given him a couple of days to make a decision.
"I now expect him to make up his mind in the next 24 hours."
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