The DOJ says that there is no factual basis for this claim:
"Both FBI and NSD confirm that they have no records related to wiretaps as described by the March 4, 2017 tweets," the government said, referring to the Justice Department’s National Security Division.
The DOJ document can be seen here.
Regarding the house intelligence committee mentioned in the comments, it doesn't seem that they are taking the allegations seriously either. Schiff called them "destructive" and "baseless", Himes called them a "mess", Rubio said that he doesn't know what Trump is talking about, Collins said she sees "no evidence" and that the commitee needs to deal with "evidence", and Burr said that they would be "guided by the intelligence and facts". Nunes seems to be the only one who wanted to make inquiries, but those did not turn anything up:
"We don't have any evidence that took place," Nunes said. "I don't think there was an actual tap of Trump Tower."