It is permissible for the one who emigrated from Makkah to stay there for three days after completing Hajj and 'Umrah, and no more than that Sahih Muslim 1352 e

Sahih Muslim 1352e
Arabic hadith text
وَحَدَّثَنِي حَجَّاجُ بْنُ الشَّاعِرِ، حَدَّثَنَا الضَّحَّاكُ بْنُ مَخْلَدٍ، أَخْبَرَنَا ابْنُ جُرَيْجٍ، بِهَذَا الإِسْنَادِ مِثْلَهُ
Translation

Ibn Juraij narrated this hadith with the same chain of transmitters.