Grujic nearly joined Bundesliga outfit Werder Bremen on Monday, but the Serbian's proposed £18 million (€20m/$23.5m) move fell through.
After lengthy negotiations between the two sides, sources told Goal that Bremen were ultimately unable to match Liverpool’s asking price.
Liverpool have been adamant that they would not entertain any loan offers for Grujic this summer, instead preferring to sell the 24-year-old outright, but the Reds eventually changed their mind as the October 20 deadline for Premier League clubs to register a 25-man squad approaches.
Having failed to sell either Grujic or Swiss midfielder Xherdan Shaqiri on deadline day, Liverpool now have 18 non-homegrown senior players available, one more than the 17 permitted in Premier League and Champions League squads.
With Grujic facing the likelihood of missing out on Liverpool's squad entirely, and being without first-team football until January, the Reds have sanctioned a loan move to Porto with the Portuguese league's transfer window still open.
Grujic will join up with Sergio Conceicao's squad after Serbia's international fixtures against Norway, Hungary and Turkey in the coming week, with an opening in the Portuguese champions' squad created by Danilo Pereira's loan switch to Paris Saint-Germain on Monday.
There is no option to buy included in the loan agreement, but the player is understood to be enthused about the prospect of testing himself at Champions League level. Porto have been drawn in a group with Manchester City, Marseille and Olympiacos.
Grujic spent the last two seasons on loan in the Bundesliga with Hertha Berlin, where he impressed while making 54 appearances and scoring nine goals.
He is highly thought of at Anfield, and impressed in two Carabao Cup appearances for the Reds against Lincoln and Arsenal this season.
The Serbian international was one of several Liverpool players, along with Shaqiri and Welsh winger Harry Wilson, who were tipped to leave the club before deadline day but ultimately stayed at Anfield.
Though Shaqiri had interest from clubs in Germany and Italy, an offer for the Swiss international never arrived. It was announced on Monday that Shaqiri was the latest Reds player to test positive for Covid-19, with the 28-year-old now entering a period of self-isolation.
Wilson, meanwhile, was looked at by a host of Premier League sides, but none of them made a bid that matched Liverpool's £15m (€16.5m/$19.5m) valuation.
After they were surprisingly hammered 7-2 by Aston Villa at the weekend, Liverpool return to action after the international break with a Merseyside derby encounter against first-placed Everton on October 17.