Is it true that Khadījah proposed to the Prophet Muhammad (sws)?
Yes, this seems to be true. History tells us that Muhammad (sws) had gone to sell some merchandise in a caravan owned by Khadījah, at that time a rich and successful business lady. She was much impressed by tales of Muhammad’s honesty (which was hard to come by in those days), which she heard from other members of the caravan. She then expressed her wish to marry Muahammad (sws), to which he showed his consent.
It needs to be appreciated that a marriage proposal can be initiated by either side. Islam has not given any directive in this regard and left the matter to the customs and traditions of a society.