The boys aged ten and eight were travelling in a Toyota Previa which crashed down an embankment after being hit by a Range Rover at around 6am not far from Junction 16 on the southbound section of the M6.
25 year old McCormick, currently playing for Plymouth Argyle, is reported as being unhurt but has been held on suspicision of causing death by dangerous driving.
"The club is aware of an incident involving one of our players that occurred on Saturday morning on the M6," read a statement on Plymouth Argyle's official website.
"As the incident is subject to police enquiries, the club feels it would be inappropriate to make any comment at this stage."