Lifelong Celtic fan Keane, 29, refused to look beyond that when asked if he would like to make the move permanent.
"I'm here until the end of the season," he said. "That's as far as I've thought about anything. I'll enjoy these few months of playing football."
And that will involve winning as much silverware as possible.
Indeed, so significant is Keane's move, bookmakers immediately slashed the odds of Celtic overhauling Rangers' 10-point lead in the SPL.
Keane said: "I'm not a betting man, so I don't get involved in that.
"But, at the end of the day, I'm here to hopefully win trophies for Celtic and that is hopefully winning the league.
"I want to be part of that and I believe, with the squad of players that are here, there's no reason why we can't."
The former Leeds, Inter Milan and Liverpool star is also looking forward to playing in an Old Firm derby.
"The Rangers-Celtic game is obviously massive," he said. "I've been lucky enough to be at the game a couple of years ago. The atmosphere was absolutely unbelievable.
"It's a game I'm really looking forward to."
Keane was presented to hundreds of jubilant Celtic supporters in the early hours of Tuesday morning, arriving at Parkhead to a hero's welcome on the stroke of midnight before addressing the throng waiting to greet him.
Describing the reception as "unbelievable", he admitted he would now be under pressure to perform, but added: "I thrive on pressure."
Despite being handed the number seven jersey worn by Parkhead legends including Henrik Larsson, he said: "Henrik Larsson obviously stands out in everyone's mind. But we're two different players."
He also insisted he knew nothing about how his loan was funded, amid rumours billionaire director Dermot Desmond had personally helped finance the move.
Keane's signing, Celtic boss Tony Mowbray's fourth of transfer deadline day, dwarfed those of Diomansy Kamara, Edson Braafheid and Paul Slane.
Monday night also witnessed the ninth departure from the club since the turn of the year, with Scott McDonald joining Middlesbrough for an undisclosed fee.
Keane signed for Spurs in 2002, making almost 200 appearances and scoring 80 goals, before joining Liverpool for around £20million in July 2008.
However, he went on to make only 15 appearances for the Anfield side and rejoined Spurs in February 2009 for £12million, taking his cumulative transfer fees to more than £70million.
He has been allowed to join Celtic after being unable to secure regular football at White Hart Lane.
He is eager to make his debut in Tuesday night's game at Kilmarnock, whose manager is looking to take advantage of the recent upheaval at Parkhead.
Keane was Mowbray's eighth signing since the turn of the year and Killie boss Jimmy Calderwood said: "There have been a lot of changes since Tony came.
"Tony must have looked at it and wanted to bring his own type of players in.
"Time will tell if they've made the right choices.
"A lot of new lads have come in and they've got to gel.
"Hopefully they won't against us."
Scottish Premier Winner 2009/10 Win Outright: Celtic 2/1