Murtagh and Cross report that United inquired about the 27-year-old powerhouse's availability in the last window, but that Newcastle were unwilling to let him go because of the swift departure of Yohan Cabaye to Paris Saint-Germain.
The authors also report that they believe Moyes sent a team of scouts to watch highly regarded Portugal international William Carvalho playing for his team Sporting Lisbon before the European transfer window closed.
Like Tiote, the 21-year-old has greatly impressed United's backroom team, and a bid could be forthcoming.
Carvalho's stock has jumped in recent months, and it is believed that both Real Madrid and Barcelona may try and capture the young talent in the summer, per The Daily Star.
United's interest will be well and truly challenged for his services.
Adam Crafton of The Mail Online also reports that Carvalho has a release clause in his contract and it would take a bid of £37.5 million to activate this.
Given the price United payed for Juan Mata, they may feel that this is too much for a defensive player.
Either Tiote or Carvalho would be tremendous captures for Moyes, and they represent the type of player that the Red Devils need immediately.
United have relied on Phil Jones to add the muscle needed in midfield for a long time now, but if he is to play in his more natural defensive role, with both Rio Ferdinand and Nemanja Vidic falling further from favour, the club will be forced to purchase a combative individual.
Both Tiote and Carvalho can fulfill that defensive midfield role, without sacrificing quality or skill.
Would Tiote fit in at United?
Tiote has featured 21 for his club this season in the Premier League, with an impressive average-passing ratio of 87 percent, per Squawka.
He has been seminal in Newcastle's success this season, recapturing the form that propelled his reputation forward when he first joined the North East giants.