Signing a third midfielder remains the primary focus following the arrivals of Andrey Santos and Youri Tielemans, but Manchester United are also weighing up a move to provide competition for Luke Shaw on the opposite flank.
Hall has impressed at Newcastle since joining on loan from Chelsea for the 2023-24 season before making the move permanent for £28m plus a further £7m in add-ons.
The 21-year-old has earned four England caps and was considered unfortunate to miss out on Thomas Tuchel's World Cup squad, and remains under contract at St James' Park until June 2029.
Robinson, meanwhile, signed for Fulham from Wigan for £2m back in August 2020 and was part of Mauricio Pochettino's USA squad during the tournament, making four appearances. The American full-back will turn 29 next month, making him older than the profile United typically prefer, and his contract at Craven Cottage runs until June 2028.
Both players represent contrasting options for Carrick as he looks to add depth behind Shaw, who remained United's first-choice left-back throughout last season. Hall offers the younger, longer-term profile but Newcastle United's reluctance to lose another key player after already selling elsewhere this summer could make negotiations difficult.
Robinson, by contrast, brings Premier League experience and reliability, even if his age places him closer to a squad option than a long-term successor.
United's midfield business is expected to take priority over any move for a new left-back, with the club keen to avoid rushing into additional deals before assessing the full picture of their summer transfer window.
With Tyrell Malacia having already left Old Trafford and Patrick Dorgu expected to continue in a more advanced role under Carrick, Shaw currently stands as United's only recognised senior option in the position, with Diogo Dalot and Noussair Mazraoui able to cover but neither considered a natural fit.
That leaves the club exposed across a long campaign that will include Champions League football, adding urgency to the search even if a deal for either Hall or Robinson does not materialise imminently.