According to Samuel Luckhurst of the Manchester Evening News, the European champions have asked to be kept in the loop regarding developments to do with any of those players.
Additionally, Madrid are said to have given the United a first-refusal option on Gareth Bale, who has been linked with a summer exit from the Santiago Bernabeu club.
"Real are mindful of United's longstanding admiration for Bale and desire to preferably sign two central midfielders ahead of next season," continued the report. "They have intimated they could be amenable to offering Luka Modric or Toni Kroos, two players whom United have considered signing in the past, in a de-facto swap deal."
Despite Madrid reportedly making it clear they are interested in a trio of Red Devils players, according to Luckhurst there's little intention of United selling.
In the case of De Gea, the club are said to be working on a new contract, with his current terms set to expire in 2020. Madrid, meanwhile, are noted to have no interest in letting both Kroos and Modric leave the club at the same time.
Per the Premier League Twitter account, the United goalkeeper is having another memorable campaign between the sticks:
Both Pogba and Martial have been subject to varying degrees of speculation recently, as both have had interesting seasons at Old Trafford.
In the case of Pogba, he was left out of the side by manager Jose Mourinho for a spell, with his omission from the starting lineup in the two UEFA Champions League matches against Sevilla particularly surprising.
Rumours about the former Juventus man potentially moving on have gathered pace as a result. Even so, Pogba said recently he has "no problem" with Mourinho in an interview with Telefoot (h/t Chris Burton of Goal).
Martial has been rotated in and out of the side more frequently than Pogba. Earlier in the season he shared a spot on the left side with Marcus Rashford, although the excellent form of Jesse Lingard and signing of Alexis Sanchez in January has meant some shifting around in the attacking third.
The 22-year-old has still managed to notch nine goals and six assists in the Premier League this season. And the United Stand Twitter account suggested United would be unwise to let some of their best prospects go:
In isolation, Bale would be an exciting acquisition despite seemingly falling down the pecking order at the Santiago Bernabeu. Fitness permitting, he can still influence matches at the highest level and the Welshman showed during his time at Tottenham Hotspur he can still have an impact in the Premier League too.
Nevertheless, United shouldn't be making room for him by moving on either Pogba or Martial, as the France internationals have the talent to be mainstays of this side for many more years to come.