Pellstri completed a move to Manchester United for £9m in October 2020 after rising through the youth ranks at Penarol in Uruguay.
The 22-year-old experienced two loan spells with Alaves, before he eventually made his competitive debut for Man United in January 2023.
After going on to make 10 appearances in the second half of last season, Pellistri remained part of the first-team set-up for the current campaign.
However, the Uruguayan has found game time hard to come by, having featured in just 14 competitive games this season.
Incidentally, 10 of those appearances have come from the bench, while he has been left out of the matchday squad in Man United's last three Premier League matches.
With Pellistri struggling to gain regular minutes, he been permitted to join relegation-threatened Granada on loan until the end of the season
While the youngster is set to return to La Liga, his agent Edgardo Lasalvia has criticised Ten Hag's treatment of his client.
Lasalvia told Sport 890: "Whether he returns to Manchester in the middle of the year will depend on the performance he shows.
"If Ten Hag continues, it's going to be difficult. Ten Hag hasn't used him, valued him, or treated him like a professional."
Although Pellistri may face an uncertain future at Old Trafford, he is still under contract until June 2025, with an option to extend by a further year.
The Uruguay international has become the latest Man United player to leave on loan in the current transfer window.
Jadon Sancho and Donny van de Beek are currently on loan in Germany with Borussia Dortmund and Eintracht Frankfurt respectively.
Hannibal Mejbri joined struggling La Liga side Sevilla earlier this month, while Alvaro Carreras and Dan Gore are also among those who have left on temporary deals.