Directors of the North Lanarkshire club started work to “ascertain whether it is possible any such incidents could have occurred at the club in the past”, in light of recent coverage around the UK.
A forensic accountant is now being brought in to examine employment records, and Police Scotland and the Scottish Football Association (SFA) have been made aware.
The club said “all information collated to date has been passed to the relevant authorities”.
It comes as an SNP MSP called on the SFA to launch an inquiry into allegations of historical sexual abuse at Scottish clubs.
James Dornan has written to SFA chief executive Stewart Regan requesting urgent action.
His call follows demands for an inquiry into the scandal from former SFA chief executive Gordon Smith.
A Motherwell statement said: “As a result of the extensive coverage relating to allegations of historic child abuse in football, the Directors of Motherwell FC began an internal investigation to ascertain whether it is possible any such incidents could have occurred at the club in the past.
“Having spoken to a number of people who had connections to the club in the period covering late 1970s and 1980s, we have decided to widen the investigation and have employed a forensic accountant to assist us with the examination of employment records and club documents from the period.
“We have made both Police Scotland and the Scottish FA fully aware of the nature of our investigation.
“We will continue with that process, but all information collated to date has been passed to the relevant authorities. The club will wait until the conclusion of the investigation before making any further comment.
“In the meantime, Motherwell FC would urge anyone who may have been affected by abuse in football to contact Police Scotland or the NSPCC helpline (0800 0232642) set up to support and advise victims of abuse.”