The German stopper committed two errors in the Champions League final which helped Real Madrid win the competition for the third consecutive time.
Although many Reds fans have called for Karius - who tearfully apologised for his mistakes - to never play for the club again, Grobbelaar believes that the 24-year-old should be given another chance to redeem himself.
"They gave me two years of second chances," the Zimbabwean told BBC Sport regarding his Liverpool days. "So why can't they give him a second chance after one game?
"They should keep him in the spotlight from next season. First game back, get him back as soon as possible."
Roma and Brazil keeper Alisson Becker is believed to be on Liverpool's radar.