Following swiftly on the heels of the British record signing of attacking midfielder Angel di Maria, Van Gaal appears to be ignoring the burning issue of a porous and inexperienced back line which has struggled badly in the first three Premier League games of the season.
Stalwarts Nemanja Vidic and Rio Ferdinand have left Old Trafford along with long-serving left back Patrice Evra. Although Marcos Rojo and Luke Shaw have been signed along with versatile Dutchman Daley Blind, Van Gaal's defensive resources look thin unless he opts to do more business before the deadline closes at 2200 GMT.
Phil Jones, Chris Smalling and Jonny Evans have struggled to adapt to Van Gaal's preferred 5-3-2 formation and Van Gaal has been forced by injuries to play 20-year-old Tyler Blackett.
He tried to recruit Arsenal central defender Thomas Vermaelen, who ended up at Barcelona, and United's longstanding interest in Germany's Mats Hummels has come to nothing.
Compounding the problems at the back is a shortage of disciplined defensive midfielders.
Spaniard Ander Herrera missed the last two games due to injury and Van Gaal has been forced to play Darren Fletcher and Tom Cleverley, a combination short of pace and genuine creative ability.
The signing of Di Maria for 60 million pounds ($99.7 million) will bring speed and invention to United's attack led by Robin van Persie and Wayne Rooney.
Mexican Javier Hernandez has been loaned to Real Madrid and Falcao's arrival could also allow Van Gaal to offload England's Danny Welbeck.
The 28-year-old Colombian, who is joining United initially on a season-long loan, is a proven marksman.
He netted 41 times in 51 games for Porto, scored 52 goals in 68 matches for Atletico Madrid and 11 in 20 appearances for Monaco before a knee injury ended his season early and ruled him out of this year's World Cup.
Fast and powerful, Falcao will give United another cutting edge but doubts remain about whether the forwards will get the service they need to show off their undoubted talents.
Van Gaal may move for Netherlands midfielder Kevin Strootman in January if he proves his recovery from a serious knee injury but by then United could be well adrift of the Premier League leaders and struggling to qualify for the Champions League for the second season in a row.