LinkedIn does not specify the limit, however, it all depends on your acceptance rate and the outstanding pending connection requests you have. To give you an idea, I have over 1500 pending connection requests pending but at the same time, I have close to 40% accept rate. The system has a glitch where it doesn't automatically remove pending connection requests (starting with the oldest), hence I went in and removed them myself. I manually removed over 1k and have about 400 left which are roughly a week old. I noticed that if they don't accept your request by the 5th day or so, they won't so I just remove anything older than a week. Of course there are some laggers who do accept after 7 days.

If you do have pending connection requests piling up, don't forget to remove them to avoid getting dinged by LinkedIn! Here's how you do it manually.