The arrival of the Icelandic defender is likely to signal the end of City's pursuit of Baker, who now looks set to stay at Villa Park.
Hordur Magnusson is set to move to Bristol City
City boss Lee Johnson had previously been keen on making a move for Baker, who enjoyed a successful season-long loan at Ashton Gate last term, but the 25-year-old now looks set to play a part in Villa boss Roberto Di Matteo's plans for the coming Championship campaign.
Nathan Baker now looks set to stay at Aston Villa
And with the impending arrival of Juventus starlet Magnusson, City's pursuit of Baker now appears to be over.
The Icelandic defender is expected to arrive at Ashton Gate for £2.5 million, which is almost certainly less than any potential bid for Baker, who still has three years left to run on his contract at Villa Park.
The Icelandic international could cost the Robins around £2.5 million
Despite lacking the Premier League experience of the Villans defender, Johnson is hopeful that the arrival of Magnusson will be enough to shore up his defence for the coming campaign.
Given that Derrick Williams and Zak Vyner can also provide cover in the centre of the defence, Johnson is understood to be confident that he has enough quality in that particular area.
Bristol City manager Lee Johnson is to assess his options for further transfers
However, the Bristol Post claims he is still keen on bringing in a right-back and is assessing his options after seeing a deal for Sunderland's Adam Matthews hit a snag.