The League wants ISPs to cut off access to FirstRow1.eu, which operates from Sweden.
The BBC understands none of the ISPs plans to challenge the court order.
If successful, the action will be the first sport-related site block in the UK.
The Premier League's move follows a precedent set by the BPI music industry body, which has been successful in having several piracy websites blocked in the UK, most notably the Pirate Bay.
In those cases, ISPs have stood firm and insisted they would only take action if ordered to do so by the courts.
The UK's major ISPs each received a letter from the Premier League outlining a possible court order, and were given a deadline of Friday to signal any intent to challenge the action.
When approached by the BBC, none of the ISPs would comment specifically on the Premier League's planned action, but all reiterated that blocking of sites would not be done voluntarily.
The situation raises additional issues for BT, as from next season it will be a major distributor of Premier League football through its new sports TV channels.
BT has paid Â£246m for rights to show Premier League football, while Sky paid Â£760m for its portion of the coverage.
Sky's ISP operation has historically been seen as taking a more sympathetic stance with copyright holders requesting the blocking of sites, whereas BT has in the past taken such battles to court on behalf of the ISP industry as a whole.
Jim Killock, of the Open Rights Group, said he worried that conflicted interests might lead to the blocking process becoming less transparent.
"All of the major ISPs now have differing degrees of conflicts of interest," he told the BBC.
"Sky, BT, Virgin and TalkTalk all supply televisions services now, so we have to expect that there will be more reluctance to be as transparent as they have been in the past."
Mr Killock also expressed concern that as the process for granting court orders gets quicker, it may lead to sites being wrongly blocked out.
"It's possible that very legitimate services will at some point be attacked by one of these orders.
"Our main concern here is that these orders should be considered slowly, and they should be subject to much more public review."
FirstRow1.eu did not respond to the BBC's request for comment.
The Premier League is to request a court order forcing internet service providers to block a popular football streaming website before the next season.