His lawyer Rudy Giuliani told Fox News that it would be wrong for Mr Trump to concede because: "There is strong evidence that this was an election that in at least three or four states, and possibly 10, it was stolen."
The Trump campaign is yet to provide this "strong evidence" but says it plans to lodge lawsuits in several key states on Monday.
Here's what we know so far.
Pennsylvania
Mr Giuliani says further lawsuits will be filed over a lack of access for poll watchers in the state.
Poll watchers are people who observe the counting of votes, with the aim of ensuring transparency. They are allowed in most states as long as they are registered before election day.
In some areas this year, there were restrictions put in place before election day, in part due to coronavirus. There are also capacity limits set to avoid intimidation.
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