In late trade on Thursday, Safeway shares traded at around $39.40. (Click here to track the grocery store chain's stock.)
Cerberus already owns Albertsons, which operates 1,000 stores and 12 distribution centers in 29 states and employs approximately 109,000 associates. The deal would greatly expand Cerberus' reach into the grocery store arena. Currently, there are 1,600 Safeway stores across the U.S. and Canada.
"This transaction offers us the opportunity to better serve customers by adapting more quickly to evolving shopping preferences in diverse regions across the country," said Albertsons' CEO, Bob Miller, in a statement.