Shaw has only played 98 minutes of football this season, with the left-back struggling with a number of fitness problems.
The 29-year-old has been missing since the start of December with a muscular problem, and he has had a couple of setbacks in his recovery.
Mount, meanwhile, has been out with a thigh issue since the middle of December, with his last appearance coming against Manchester City in the Manchester derby at the Etihad Stadium.
There have been suggestions that both players could be out for the remainder of the season due to the nature of their issues, and Amorim has admitted that neither are close to returning for the Red Devils.
Neither Shaw nor Mount close to featuring for Man United
"No. He's doing his rehab but we don't have a date for him yet," Amorim told reporters when asked about a potential return date for Shaw, who had his latest setback in his recovery three weeks ago.
Meanwhile, when questioned on Mount, the manager said: "Not specifically, no. I think he's closer than Luke Shaw but we don't have a specific date to return."
Mount has made 12 appearances for Man United this season, including seven outings in the Premier League, and he was expected to be a key player under Amorim, with the Portuguese believed to value his high-energy style.
The Englishman made the move to Old Trafford from Chelsea in the summer of 2023, but he has been restricted to just 32 appearances in that time, scoring once and providing one assist, with the Red Devils not getting much value from the initial £55m that they spent to secure his signature from their Premier League rivals.
How many Man United players are currently on the sidelines?
Man United have an injury crisis at this moment in time, with nine players set to be sidelined for Wednesday's Premier League clash with Ipswich Town at Old Trafford.
Lisandro Martinez and Amad Diallo are both out for the season, while Kobbie Mainoo, Toby Collyer, Jonny Evans, Tom Heaton and Altay Bayindir are on the sidelines alongside Shaw and Mount.
As a result, there will again be academy players involved in the squad against Ipswich, and 17-year-old Chido Obi is battling to make his full first-team debut after two substitute appearances against Tottenham Hotspur and Everton.
Written by
Matt Law