United and Liverpool have won 20 and 18 league titles, respectively, along with a string of other domestic competitions and a combined eight European Cups.
However, this year they meet at the last-16 juncture of the Europa League looking to kick-start their season and boost their chances of reaching the continent's top table.
Poor league displays mean European football's second-tier competition looks England's most successful clubs' best chance of Champions League qualification, but United boss Van Gaal believes their previous success came during a bygone era.
"In football, it's normal,'' the Reds manager said of teams falling from the summit.
"It's not normal that one team is dominating for 20 years in a row (as) the champion."
When put to Van Gaal that Liverpool and United had dominated for decades, he responded: "It was another time, it was another time.
"You live in the past, you live in the past and you have to live in the present, I think."
That current state of affairs domestically means the Europa League may well offer both clubs their best chance of reaching the Champions League.
United sit sixth in the Barclays Premier League, three points off the top four, and Liverpool are a place and three points worse off, albeit with a match in hand.
However, Europa League glory would guarantee Champions League qualification regardless of league performance, adding extra motivation - if any was needed - for the last-16 tie.
"Liverpool - Manchester United is always a big game traditionally," Van Gaal said ahead of Thursday's first leg.
"It's historic and, especially because both teams fight for a Champions League position, it's a big game for both sides."
Source: PA