Costa, 28, is believed to have been unsettled by a big-money bid from the Chinese Super League, which would make the Spain international the highest-paid player in world football.
It is understood that Costa has been dropped from the Chelsea squad for their clash with Leicester City this weekend after a falling-out with head coach Antonio Conte, which has thrown the striker's future into doubt.
Souness believes that Chelsea and Costa could sort out their differences, but the Scot claims that losing the striker could cost the Blues the Premier League title this season.
"This is the very last thing Chelsea need. He is playing out of his skin. They lose him and all of a sudden they are not going to win the Premier League," Souness told Sky Sports News. "If sense prevailed maybe he could stay until the end of the season. There has to be a way around this where everybody can be happy."
Costa was strongly linked with a return to Atletico Madrid last summer, but ultimately remained at Chelsea and has fired the Blues to the top of the Premier League table with 14 goals and five assists in 19 league matches this term.