The duo are available after parting ways with Mamelodi Sundowns and Orlando Pirates respectively and are eager to secure moves abroad ahead of the new season.
Pyramids are in the market for a proven goalscorer after Congolese striker Fiston Mayele left the club as a free agent following the expiry of his contract.
The 32-year-old who scored 54 goals in 125 matches while in Egypt recently represented DR Congo at the FIFA World Cup before becoming available on the market.
The public broadcaster understands Shalulile, Sundowns' second all-time leading scorer behind the legendary Daniel ‘Mambush’ Mudau, is keen to revive overseas opportunities after previous talks with Esperance and Wydad Casablanca failed to produce a move in January.
Mabasa, meanwhile, spent the second half of last season on loan at Stellenbosch FC but could not agree terms on a permanent stay and is currently training on his own while assessing his next move.
Both spent almost six years at their previous clubs.
Information gathered further indicates that both forwards have now been presented to Pyramids as potential reinforcements, although no decision has yet been taken on whether Mokwena wants to reunite with either player in Cairo.
Both strikers continue to attract interest from clubs in the Betway Premiership, but their priority is to continue their careers outside of South Africa.
With the transfer window open and Mokwena expected to reshape his squad, it remains to be seen whether Pyramids will pursue either Shalulile or Mabasa as they look to strengthen their attacking options ahead of the new campaign.