Singer Tomlinson, who played for Doncaster's reserve team earlier this year, had planned to take over the League One (third tier) club with former owner John Ryan.
The pair had set up a crowd funding scheme to support the plan but that initiative had raised less than 40 percent of its target on Friday despite the Tomlinson Ryan Trust putting in a "six figure sum" to get the ball rolling.
Tomlinson said on his Twitter feed that he was "absolutely gutted" that the deal was not going ahead to buy a team he has grown up supporting.
Ryan blamed the Football League for blocking the deal.
"They have made it so difficult now that unless you have a bag full of cash you are going to get turned down," he told BBC radio.
The League said it had a duty to ensure that clubs were financially stable.
"In any club takeover it is a requirement for the prospective purchaser to provide a business plan and to demonstrate that the funding is in place to deliver on that plan," it said in a statement.
"In this case, this fundamental requirement has not yet been met."
Tomlinson, 22, is one of five members of boy band One Direction, a group assembled on British talent show "The X Factor" in 2010.
One Direction was the first group in the history of the U.S. Billboard Top 200 chart to debut at No. 1 with its first three albums.
(Writing by Keith Weir, editing by Tony Goodson)
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