The 20-year-old provided both assists for Elias Melkersen’s brace in the Scottish Cup quarter-final victory over Motherwell last weekend and was praised by his manager for his performance at Fir Park.
Hibs have an option to buy the Bulgarian Under-21 internationalist this summer as part of the loan arrangement and Maloney is keen to activate the clause.
"I think that will have to be discussed pretty soon, yes,” the Easter Road boss told the Evening News.
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"It's difficult to really say anything until we've actually got something definitive but from my side, I'm really pleased with how he's playing.
"I’m really pleased too, with how he’s progressing. He works extremely hard and like Elias he’s one of the first to arrive and last to leave the training centre, so I hope that continues.
"What I really see in Sylvester is a real hunger to improve so if that continues, then I certainly hope we’ll continue to work with each other next season.”
Jasper’s performances since swapping Craven Cottage for Easter Road in January have seen him called up to the Bulgaria Under-21s for their UEFA European qualifying matches against the Netherlands and Wales.
The winger qualifies for Bulgaria through his mother and has already won two caps for Aleksandar Dimitrov’s side. He could feature in the matches against the Dutch at the Stadion Aleksandar Shalamanov in Sofia on Friday March 25, and against the Welsh at Newport County’s Rodney Parade ground four days later.