Winger Thompson is expected to become a free agent this month having lost his place in Celtic's first team and Dennis Wise is ready to do battle with a number of clubs for his signature.
United have also been linked with a move for striker Maccarone but their interest in netting the forward on loan is likely to come to nothing by his wish for a return to his native Italy.
Maccarone has failed to win a regular position under Boro boss Gareth Southgate and will be allowed to move on during the transfer window.
The 27-year-old said: "I want to change and maybe come back to Italy. I'm not perfect and for sure I haven't had my best performance."