Carrick last played on 17 February in Manchester United's FA Cup win over Huddersfield.
The La Liga side have failed in their three previous attempts to progress from the competition's last-16, including falling at this stage against Leicester last season.
On announcing his decision to retire, Carrick said: "I think it's pretty much already been said, to be honest with you".
Celtics' Kyrie Irving suggests longer period of rest for sore knee
The Celtics fought hard for a 50-40 halftime lead, limiting Oladipo to just 3-for-9 from the field in the first half. While not as important as Kyrie Irving , Theis is still an important factor off the Celtics bench.
The Old Trafford club captain told a news conference on Monday: "There comes a time, wether you like it or you don't like it, that your body tells you it is time to stop playing football".
Manager Jose Mourinho revealed in January that the former England worldwide will take up a coaching role with the first team at the end of the campaign.
Do you ever have any question about anything you wish to ask and get answer? We're still talking about it, to be honest, so there's nothing to totally confirm as yet. But it's looking likely, yes'.
Coutinho milite pour un retour de Neymar — Barça
Ciblé par le Real Madrid (quid du Barça?), le natif de Mogi das Cruzes n'a pas mis le feu aux poudres pour partir. Qu'on se le dise, Ivan Rakitic serait aux anges si Neymar (PSG) faisait son come-back au FC Barcelone.
The 36-year-old has been restricted to four appearances this campaign due to an irregular heart rhythm, which forced him to have surgery in November. It took a little while to get over. But he needs to get his form back, he needs to be playing, and he needs to be standing out in games like Liverpool at Old Trafford. "If I finished the session one minutes before it wouldn't have happened". I understood after getting back fit that I wouldn't be playing as many games as perhaps I might have done, but that's something that I understood. There were some times there, two or three days, when I wondered whether I would carry on playing or not, is it worth it or not? "I still see myself as a player - for now anyway - and I am still enjoying training and being out with the boys".
"With people like Scott (McTominay) and some of the younger boys, I'm just trying to help them adapt".
Bills Move Up in First Round by Trading Cordy Glenn to Bengals
Many thought the Bengals may use their 12th overall pick on a tackle, or an offensive lineman of some sort at the very least. The rookie certainly showed enough promise to make Glenn expendable, especially considering his contract and injury history.