The Daily Mail says United are targeting midfield pair Elliot Anderson and Morgan Gibbs-White.
United have long had Anderson on their radar, having made enquiries during the January market. But now Gibbs-White has been added to the shopping list.
Forest are preparing to lose Anderson over the summer and have slapped an initial price-tag of £100m on his shoulders.
In Gibbs-White's case, the midfielder eventually resisted a £60m move last summer before penning a new contract. That new agreement is said to include a buyout clause, which comes into effect this coming transfer window.
Any success in moving for the Forest pair is likely to hinge on United finishing in the top four and qualifying for the Champions League this season.