Van Gaal is hoping the injury-hit Colombian can finally display the qualities that have made him one of the most feared strikers in world football - especially important for United with Van Persie struggling for form.
Falcao's loan spell at Old Trafford has been disrupted by injuries but Van Gaal is hopeful he will be in the squad for the visit of Hull on Saturday.
Asked if Falcao's return would increase the pressure on Van Persie, who was substituted against his former club Arsenal last weekend having had just 13 touches of the ball, Van Gaal said: "Every player in my selection has to fight for his position and I shall always take the best of the players and it must also be suitable for the mix of players.
"So it is also an obligation of a player that he does that."
It is not just Falcao who is poised to provide a huge boost for United, but Argentina defender Marcos Rojo is also in contention after being out with a shoulder injury
Van Gaal told a news conference at United's training centre: "We have to wait and see until the last training session of course
It's always difficult to say but we have good news, yes
You have to read between the lines.
"I have to train the last session and I live day by day at this moment
So maybe Falcao can come back in the 18 [matchday squad], maybe Rojo can come back in the 18
That's it I think."
Van Gaal was also careful to provide an exact statement on England full-back Luke Shaw, who suffered an ankle injury against the Gunners
A week ago the United manager's comments on Daley Blind's knee problem were misinterpreted and led to the club's 3.5million Twitter followers being erroneously advised the Dutch player was out for six months.
Van Gaal said: "Last time I have said something and it was not interpreted so good so I have asked my medical advisor and maybe Manchester United Twitter account can pay attention to it!"
The United manager then read from a prepared statement saying: "Luke sustained an ankle ligament injury but with no serious complications and he will be out for the next few weeks because of this."
He then added: "I have said that also with Daley Blind it will not be six months."
Phil Jones (shin), Jonny Evans (ankle) and Rafael (hamstring) are all still out injured.
Hull boss Steve Bruce will mark his 700th match in football management with a timely trip to Old Trafford and says experience has taught him not to panic about the Tigers' recent plight.
There could be no more fitting arena for former Manchester United star Bruce - who was first appointed player-boss at Sheffield United in 1998 - to mark his managerial milestone, but his mind will be more on arresting his side's run of three consecutive defeats.
After a bright start and impressive transfer outlay it has come as a blow to Bruce but, despite being linked with a series of reinforcements in the new year, he is adamant he has a strong enough squad to pull out of their recent poor form.
Bruce said: "I genuinely haven't looked at January yet - I'm happy with the squad we've got
We made big changes in the summer and some of those players are just starting to bed in and I'm sure we will get better as the season goes on."
"It's all about doing all you can to keep the squad as good as it can be
Of course when you get beaten a few times the doubts creep in but you've got to keep everybody positive and make sure they believe in what you're doing.
"There's not a lot wrong and we've just got to stay with it
We've got a really difficult run of games and now we're coming to a really critical part of the season."
Bruce has received a major blow with the news striker Abel Hernandez will miss the United clash and probably also Wednesday's trip to Everton due to flying home to Uruguay to be with his partner for the imminent birth of their child.
Gaston Ramirez is suspended after his sending-off against Spurs but otherwise Bruce at least has the relief of knowing he has no new injury worries to contend with.
Bruce is yet to earn three points at Old Trafford in his managerial career and if he is starting to fancy his chances in light of United's current travails, he would not reveal his hopes ahead of his return.
"They've just had a great result at Arsenal and they're very quietly creeping up - they've had unbelievable injuries which they seem to have dealt with," said Bruce.
"But we went to Arsenal and Liverpool and picked up a result and we've got to remain positive and hope that we can play like we did in those two games and make sure we take something from the game."
Source : PA
Source: PA