It is believed that the agreement will be made permanent when the transfer window re-opens in January.
The deadline for pushing loan deals through in England is due to pass on Thursday, so Rovers are keen to get everything put in place.
It was their hope to get something done earlier in the week, but King's involvement in United's UEFA Champions League clash with Galatasaray caused a delay.
Blackburn are, however, now clear to add the 20-year-old to their attacking ranks.
King has impressed for the Norway national side this season and has picked up useful first-team experience during loan spells at Preston, Borussia Monchengladbach and Hull City.
He was handed his Champions League bow by United in Turkey on Tuesday, but he is not considered to be irreplaceable by Sir Alex Ferguson.
Rovers are prepared to offer him the opportunities he craves, as they seek promotion back to the Premier League, and there could be further deals with United to come - with Henning Berg known to have held talks with his former bosses at Old Trafford prior to taking the Ewood Park hot-seat.