The toy and game retailer said its shops in Livingston, Aberdeen, East Kilbride and Kirkcaldy are among the stores to be closed early next year, putting 800 jobs at risk UK-wide.
The CVA, which has to be approved by its creditors, could result in the loss of up to 800 jobs.
Staff found out about the closure in a synchronised announcement across the company's 106 United Kingdom stores this morning - creating uncertainty about their future just before Christmas.
The retailer said that all efforts will be made to redeploy team members where possible.
Mr Knights said: "Like many United Kingdom retailers in today's market environment, we need to transform our business so that we have a platform that can better meet customers' evolving needs".
Staff are being briefed on the upcoming changes, and no details of affected stores will be released until this has finished.
TOYS R United States has stated that the Tamworth Ventura Park store is one of the 26 it is planning to permanently close in its move to cut costs.
It detailed how Toys R Us, which employs 3,200 people, plans to restructure using a process known as a company voluntary arrangement with its creditors.
"We will continue to honour gift cards and Take Time To Pay agreements and there will be no change to our returns policy".
"Like many UK retailers in today's market environment, we need to transform our business so that we have a platform that can better meet customers' evolving needs", said Steve Knights, managing director of Toys R Us UK.
Alvarez & Marsal is restructuring advisor for Toys R Us, while Kirkland & Ellis is principal legal counsel.
"The decision to propose this CVA was a hard on, but we determined it is the best path forward to make essential changes to the business".
Toys R Us made a £500,000 operating loss on sales of £418m previous year.