I read this story a long, long time ago. Maybe sometime in the 1990s (and I suspect it was quite a bit older). I read it an anthology I checked out from a public library. The story was quite short (I suspect it would be somewhere in the range of 10-20 pages in mass-market paperback), written in English, and I remember the plot pretty well.
The story is told in the first person by a man living in a U.S. city. He feels he isn't getting anywhere in life, and he has decided to try to sell his soul to the devil in exchange for certain material considerations. In other words, if he can have lots of fun in this life, he'll take his chances on learning to tolerate conditions in hell in the afterlife.
He looks in the phone book to find a likely place to start. I think he is working on the plausible theory that the local representatives of the Devil would naturally be passing themselves off as a modern law firm. So he flips to that section of the yellow pages and looks for anything suspicious. He spots something that has names resembling variations on nouns or proper nouns commonly associated with devilish and infernal subjects. I don't remember them, but for the sake of argument, let's say the firm was called "Hellman, Diablos, Abaddon, and Synne." (I am sure that he found a firm or company with a suspicious choice of names for the partners; I just am not 100 percent sure that it was advertising itself as a law firm.)
The protagonist spends some time writing up a description of his soul. He believes it is still in fairly good shape, and thus would be a real acquisition for Hell, instead of something which the Devil was already expecting to get. Having done so, he goes to the firm I mentioned and makes his sales pitch to a partner. (Or possibly the Devil himself -- I don't remember just how important the listener seemed to be.) He is told that he has made a very good presentation and this listener is willing, in principle, to agree to grant a wide range of wishes (relating to worldly wealth and the like, I believe) in exchange for getting the protagonist's soul later on. I think there was a hard-and-fast time limit mentioned, along the lines of: "One year to whoop it up, and then it's time to pay for your fun."
However! The protagonist ends up retaining legal counsel of his own to help make the written form of the contract airtight before they actually sign anything. (This precaution may, in fact, have been suggested by the guy who agreed to buy the soul.) So he finds another law firm and those lawyers start hashing out the details with the lawyers from Hellman, Diablos, Abaddon, and Synne. A page or two of the story (at least) then describes various excuses for delay before the actual signing, such as one of the protagonist's lawyers telling him in early May, "They forgot to initial a revised page," and then telling him a few weeks later: "We forgot to initial a revised page!" Meanwhile, the narrator is still fending for himself -- I think he even gets a pretty good job. (He was either unemployed or had a very bad job when he first decided to sell his soul.)
Finally -- I think they have not yet sat down to sign a final draft of the contract -- the protagonist gets an unfriendly notice in the mail from Hellman, Diablos, Abaddon, and Synne. It says something to the effect that since X amount of time has passed (I think a full year), the deadline is already past and Hell is planning to foreclose on his soul very soon. Shocked, the protagonist calls his own law firm, and is told that the guy he originally spoke to is taking the position that the clock started ticking on the first day of discussions, when they "agreed in principle" to a sale, and shook hands on it. From that moment onward the protagonist could, in theory, have made a wish for a million dollars cold cash, or whatever, and Hellman et al. would have honored their end of their bargain. It is not their fault if he failed to avail himself of the opportunity. Now it's time to pay the piper.
Naturally, the narrator feels he's been cheated, and wonders if this contract would hold up in court. At the very end of the story, he says he has just been consulting the yellow pages again, and has decided to place himself in the hands of new legal counsel, with a firm named something along the lines of Angell, Gabriel, Raphael, and Salvador, Attorneys at Law. (Again, I'm just improvising; I don't recall the exact names. Something that suggested a heavenly connection.)
Note: Before I bothered typing out all of the above, I did make some effort to find the answer to my own question by Googling. The problem is that "pact with the devil" and "selling his soul" stories have been done zillions of times. For instance, I took the time to read the Wikipedia page called Deals with the Devil in popular culture, and I'm pretty sure the story I'm trying to trace is not mentioned on it. (I mention this to save you the trouble of searching through that page yourself!)