The Prophet ﷺ said, "None of you should propose marriage over the proposal of another."
أخبرنا قتيبة قال حدثنا الليث عن نافع
عن النبي ﷺ قال لا يخطب أحدكم على خطبة بعض
No references are available.
Muslim narrated it in Kitab al-Nikah, chapter on the prohibition of proposing marriage over a brother's proposal until he permits it or withdraws, hadith no. 1412, from Qutayba, with this wording. It also appears in al-Kubra, hadith no. 5354. Bukhari narrated it, hadith no. 5142, from the hadith of Nafi, with this wording.