BT chief executive Gavin Patterson has indicated they may consider bidding for rights to broadcast Champions League matches from 2015.
Sky paid around £240million to share live coverage of the showpiece European matches each week, with ITV's £160m giving the free-to-air-broadcaster first pick of Tuesday night fixtures.
The process of bidding for rights to broadcast Champions League from 2015 to 2018 in the UK is imminent.
BT Sport is expected to make an application following the success of its new dedicated channels covering the Barclays Premier League, Scottish top flight football and Aviva Premiership rugby union.
Speaking at the Leaders in Football 2013 event, Patterson said: "We are happy with the content we have got, but we also recognise there is much more we could do.
"This is a long-term strategy for us and you can expect us to do a lot more in the future if the right opportunity to create value presents itself."
The BT chief executive continued: "We are exactly where we hoped to be at this time in terms of audiences, but in terms of what we set out to achieve, our goal was not to be number one, it was to be number two.
"If I look at the amount of live programmes we have got on the channels, it is pretty good and compares very well with Sky.
"We look at all rights, there is nothing special in that respect around the Champions League.
"There are other rights available at the moment as well as over the next couple of years and we will look at them and assess whether we feel as if they can improve the overall composition, which is what you would expect."
BT Sport is paying some £246m a season to broadcast 38 Barclays Premier League games, with 18 top picks which on Thursday was announced would also include the Boxing Day fixture between West Ham and Arsenal at 3pm followed by Manchester City versus Liverpool, with Southampton's home game against Chelsea and then Manchester United tackling Tottenham on New Years Day.
Patterson added: "We believe we can co-exist with Sky. Our success does not require their failure, to think otherwise markedly underestimates the scale of the opportunity in this market.
"Our long-term aim is to make ourselves an immovable part of the broadcasting landscape and we are quietly confident we can succeed where others have not.
"We have got the rights to things people generally want to watch, we have got creative teams which are producing compelling and imaginative programmes, a terrific offer, free to BT customers and accessible to everyone else if they want it.
"With the technology, the best is yet to come and this is just the very beginning."