Keita, 22, scored 16 times in 35 appearances for Lazio last season, but the Senegal international will be out of contract at the end of the 2017-18 campaign, and is said to be refusing to sign a new deal.
Inter Milan have been strongly linked with a move for the attacker in recent days amid speculation that Ivan Perisic is heading for Manchester United, but Lulic is still 'hopeful' that an agreement can be reached.
"I hope there's a solution which will please everyone - Lazio, the lad and us. We're Keita's teammates, we often talk but that stays in the dressing room," Lulic told reporters.
"We want the strong players to stay, and Keita is one of those. We do what we do on the pitch, then I don't know if the president and Keita can agree. We want to work calmly, but the transfer market is open to August 31. Players can come and go, I repeat - we want to work calmly."
Keita turned out for Barcelona's youth teams between 2004 and 2011, before joining Lazio.