The public broadcaster understands negotiations have gathered momentum this week after Chiefs improved their offer following several rounds of discussions involving player-swap proposals and a cash component.
Talks had previously centred around the inclusion of striker Ashley du Preez and at least one other player, but Stellenbosch remained reluctant to sanction a move, preferring either an overseas transfer or allowing Phili to see out the remainder of his contract.
However, indications are that the two clubs have now aligned on the broad framework of a deal, although a number of finer details still need to be finalised before the transfer can be concluded.
Should those outstanding issues be resolved, Chiefs will be in pole position to complete the signing before the transfer window closes in September.
Indications are that Phili is highly rated by both sporting director Kaizer Motaung Jr and head coach Fernando da Cruz, who has prioritised the recruitment of a versatile wide attacker capable of operating on the wing or in a supporting role behind the striker.
While the move has not yet been officially completed, the latest developments leave Chiefs as clear favourites to secure the services of one of the Betway Premiership's most exciting attacking talents.