"In football surprises are the order of the day, but we speak every day with the player and I think that a positive resolution will come before the end of the season, let's say before the end of May," Sabatini told the Corriere Dello Sport.
"After that the World Cup begins and things would become altogether more complicated."
Back in January, PSG coach Laurent Blanc admitted that Pjanic was a target for the Ligue 1 champions, and Italian media has been rife with rumours that he would be moving to the French capital in the summer.
Roma are second in Serie A and have secured qualification for next season's Champions League group stage after winning nine games in a row.
They are five points behind Serie A leaders Juventus, who travel to relegation-threatened Sassuolo on Monday night looking to increase their lead to eight with three games left to play.
The extra money that will come from playing on Europe's biggest stage should help Roma keep their prized assets, and Sabatini also revealed that they will strengthen their squad through the summer.
"We will bolster the squad, and I don't think we will need to sell in order to buy," he added. "I don't know what our budget is because I haven't yet spoken about it with (club president James) Pallotta."
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