The youngster has been impressive in an attacking midfield role for the reserves but has yet to make a first team appearance for the Foxes.
Verma joined up with the Crewe squad yesterday and started training today.
Meanwhile, Joe Mattock has been the focus of further newspaper speculation, this time being linked with a move to West Bromwich Albion.
Also, It has been speculated in the tabloids today that Nigel Pearson is keen to sign Ghana striker Matthew Amoah.
The 29-year-old currently plays for NAC Breda of the Netherlands.