The unsolicited Dish offer trumps a $2.97 a share bid from Sprint made in December.
In a press release, Clearwire said it will hold discussions with Dish, but "its ability to enter into strategic transactions is severely limited by its current contractual arrangements."
"We look forward to working with Clearwire's Special Committee as it evaluates our proposal," said Tom Cullen, Dish executive vice president of corporate development, in a statement.
Sprint in a letter to Clearwire called the Dish proposal "illusory, inferior" to the Sprint offer and not viable because it cannot implemented in light of Clearwire's current legal and contractual obligations."
What are the stocks doing now?
Clearwire shares were halted pending the news, then shot up 10 percent when they resumed trading. Click here for the latest after-hours quote for Clearwire.