Champions Manchester City want to sign United's England international star Kalvin Phillips who is also attracting the interest of Paris Saint-Germain.
The French powerhouses contacted the Whites last Friday with an enquiry regarding the midfielder's availability and price.
Leeds are yet to receive a bid for Phillips, or for Raphinha who is a key summer target for Spanish giants Barcelona although the Camp Nou side may face competition from Arsenal to sign United's Brazilian international winger.
Tottenham Hotspur and Chelsea have also been credited with interest in Raphinha and former Whites star Beckford admits there is a very real possibility that both Phillips and Raphinha will leave the club this summer, even though Leeds remain keen to keep both players.
Beckford, though, says reluctantly that Leeds should not hold the talented duo back should they wish to push on and further their careers and is taking a "glass half full" approach to the potential situation of losing both this summer.
Beckford believes the sale of Phillips and Raphinha would generate at least £100m, which the ex-striker says could be reinvested in not two but three quality players.
"It would be a horrible situation, don't get me wrong," Beckford told the YEP, pondering the prospect of both Phillips and Raphinha leaving in the same summer.
"It would be horrible from a fan's perspective and from a personal perspective as well because they're both great lads.
"But also you can't hold them back because they are both extremely driven to succeed and to be successful.
"They want to play international football, which they both do but they both also want to contend and contest for trophies and individual accolades.
"You can't hold them back, especially for everything they've done for us as well.
"On the other side of that, what we get back in return, if we do end up in the worst case scenario of losing both of them, we're looking at circa 100 million pounds coming back into Leeds United.
"That can then get reinvested into the squad to help reinforce in those areas that will be missing those two guys, but also maybe another area as well.
"We'll be losing two but we could possibly end up gaining three.
"I'm a glass half full person.
"I want to see them stay, I do not want to see them leave.
"However, if they do end up leaving then that's exactly what I would say what would be the case on the back end of it."