Speaking at the MediaGuardian Changing Media Summit in central London, Thompson said that "although we are not there yet", there is the potential for a partnership - one that would be "beneficial to both parties and which could play a significant part in addressing Channel 4's funding issues".
He also revealed the BBC is talking to the Press Association and several unnamed newspaper groups about adding BBC content to their print and digital products.
Last year, the BBC and Channel 4 started talks on closer collaboration as a means of securing Channel 4's future and sharing BBC resources more widely across the UK TV sector.
And earlier this year, communications minister Lord Carter's interim Digital Britain report suggested a new, enlarged public service broadcaster could be created, with Channel 4 at its heart, as a means of providing public service content beyond the BBC.
Thompson accepted questions needed to be addressed about the competitive impact of such a proposed partnership but said: "I would not jump" to the conclusion that these are questions "that cannot be addressed".
He added: "Our emerging answer to that challenge is the idea of partnership, of redefining the relationship between the BBC and the rest of UK media - which historically has been based on rivalry and competition - so it focuses much more on collaboration and the sharing of the benefits the licence fee confers."
Thompson also revealed the corporation plans to make new cutbacks over the next three years. He is proposing a budget that includes a further £400m of what he labelled "painful cuts" and reductions in expenditure, ranging from freezing senior manager pay and withdrawing discretionary bonuses, to the amount the BBC pays top talent.
He said: "I say this not to claim that the BBC faces the same scale of financial challenge as some of our commercial colleagues. We don't. But the picture of a BBC swimming with cash and people able to make additional savings at the drop of a hat is simply out of date."
.jpg)
.jpg)