Officials at Trigoria are finalising the last details of three renewals considered essential by head coach Gian Piero Gasperini.
Dybala's new deal is close to being signed, even though the Argentinian is currently on holiday in Argentina.
An agreement has been virtually reached, with only the official announcement still to come.
Dybala's representatives have already told Boca Juniors that the forward will not consider a return to Argentina at this stage of his career.
The agreement is for a one-year contract extension, with the option of a further season, at €3 million net per year.
Celik's situation has also been resolved after the Turkish full-back revised his earlier salary demands and accepted
AS Roma's proposal.
His new contract is expected to pay around €2.5 million net per season, up from his current €2 million.
Pellegrini's renewal is more complex, though talks have officially begun.
Sporting director Tony D'Amico has already met the midfielder's representatives to lay the groundwork for an agreement.
The length of the contract and its financial terms still need to be finalised, but there is shared optimism that the two sides will continue together.
Further talks are expected in the coming days as Roma look to reach an agreement quickly.
None of the three situations is expected to affect the start of the new season, with Dybala, Celik and Pellegrini all due to report for pre-season training on 13 July.
Once these renewals are completed, Roma's attention will turn to Gianluca Mancini and Bryan Cristante, both of whom have contracts expiring in 2027.
Talks over their futures were already set in motion in recent months and will resume once the current priorities are resolved.
There is no particular urgency on the Mancini and Cristante situations, but Roma intend to address them well in advance to secure two more key figures in Gasperini's squad.