Carrick said the position was “not a huge concern at the moment” and he felt there were options available to them that provided them with variety in attack.
“We can still be dangerous,” the 44-year-old said.
“Matthias [Cunha] Has taken that role and created big problems and had big moments. When he plays wide, he’s hard to stop one-on-one.”
But Cunha is happiest moving away from the touchline and prefers to take the ball deeper or into more central positions.
In the junior ranks, Gibraltar international James Scanlon was virtually an ever-present in the Premier League 2 team for the first half of the season and is capable of playing an attacking role on both sides of the pitch, but he has now joined League Two promotion chasers Swindon on loan.
England Under-20 international Shea Lacey made a big impact in three substitute appearances for the senior team, but he prefers to play on the right. In any event, he has featured only once since being sent off in the FA Cup third round defeat by Brighton on 11 January, when he was an unused substitute against Fulham last month.
Some supporters will claim that United were wrong to get rid of Sancho or Antony.
Some believe Amorim could have handled the Garnacho situation better, although the Argentina international has yet to impress consistently at Chelsea, while Rashford’s time at his boyhood club was going well.
Yet, at a time when United are trying to control their budget and cut costs across the club, the wide-left position highlights a historic weakness in their recruitment strategy.
It also questions the wisdom of appointing a coach like Amorim, whose tactics were vastly different from what fans were used to.
United were set to sanction a £65million contract for Antoine Semenyo in January, but the former Bournemouth man opted to join Manchester City instead.
Amorim wanted to use the money elsewhere in his squad. United’s denials suggest they are targeting specific areas, and the left side of their attack is one of them.
They are among a number of high-profile Premier League clubs linked with a move for RB Leipzig’s 19-year-old Ivory Coast international Yann Diomande, who is expected to cost around £70million if he opts for a summer move.
Newcastle’s Anthony Gordon has also been mentioned, although it is unclear whether United are interested in the England international.
United’s situation is complicated by the fact that they are prioritizing bringing in at least one and possibly two central midfield players.
Veteran Brazil captain Casemiro is leaving at the end of the season and £50m Uruguay international Manuel Ugarte has made just three substitute appearances under Carrick – a total of 27 minutes.
No changes can be made until the transfer window opens, so, for now, Carrick will have to make the best of his current options.
“We’re always thinking about the right scenario to mix players together and make connections and see how it fits on the pitch,” he said.
“There are different ways to do this and we have really good options on the front lines.”