The closest thing we have to that is the posting system in American and Japanese baseball. When a Japanese player wants to play in the States but is still under contract, he asks to be "posted" by his team. That's just a way of saying, "Hey, this guy's on the market. Who wants him?" When that happens, each MLB team submits a confidential bid to the player's Japanese club for exclusive negotiating rights. The team that bids the most then "wins" the right to pay all that money to the Japanese club and then negotiate a contract on top of that.
The most famous example is from this past season when the Red Sox bid 52 million to the Seibu Lions so that they could give a 60-something million dollar contract to Daisuke Matsuzaka. That's definitely the largest amount of money exchanged since the process when into effect. This posting fee is obviously a few million pounds more that the payment for Torres (£22 compared to roughly £26, or has the dollar sunk even further since I was in London?), but I would imagine that there are plenty of players brought in from other teams that cost more than Torres, right?
As far as the NBA goes, the only time you'll see a trade for money is when a good player is traded for a decent-to-bad player with a huge but expiring contract. In this sense, a team is trading talent for impending salary cap space, which they can use to spend more freely.
In football... well, football teams almost never make trades. It's really not even worth talking about. They might trade draft picks once in a while, but money usually isn't the motivating factor there.