The Red Devils are in the process of drawing up summer recruitment plans after handing a three-year contract to Ole Gunnar Solskjaer.
With the uncertainty surrounding their managerial post ended, attention can focus on strengthening a squad which is expected to see big money invested in it.
Various targets are being mooted for United, but they have been told to look close to home for two potential additions.
Hudson-Odoi is sparking plenty of speculation at Chelsea, as Stamford Bridge chiefs prepare to enter a two-window transfer ban, while fellow teenager Phil Foden is struggling for competitive minutes at Manchester City despite being tied to a new long-term deal.
“Solskjaer should be looking at the potential Financial Fair Play problems that Manchester City and Chelsea may be having and try to sneak in to pinch the best young talent in Europe,” Cascarino said in The Times.
“Why not go to Phil Foden or Callum Hudson-Odoi and say ‘Look at [Marcus] Rashford, look at Tahith Chong – we are going to give young players a chance, come and play for us’.”
United have also been urged to step up their interest in another exciting prospect that has earned senior international recognition with England of late, with Jadon Sancho already said to be registering on the radar at Old Trafford.
“If United think they can get him then why not try and sign Jadon Sancho from Borussia Dortmund,” added Cascarino.
“They would probably have to break their transfer record to do that.”
Such a gamble is, says Cascarino, worth taking, with United needing to change their recruitment model as they build towards what they hope will be a brighter future.
“United have tried the approach of big names and big signings, but United are about something more than that,” said the former Republic of Ireland striker.
“After all, why did they consider Tottenham Hotspur manager Mauricio Pochettino? Because they wanted a manager who could mould and improve players and build a dynasty.
“This approach has to filter into the plans for summer signings.
“United should be going after players like Aaron Wan-Bissaka from Crystal Palace and Bournemouth’s David Brooks – young players who will want a chance to prove themselves at the highest level, who can add something to United’s squad.”