The San Siro giants have lifted the famous trophy on 10 occasions between them - the most recent instance coming in 2010 when Jose Mourinho's Inter completed the treble, having ousted Messi's Barcelona in the semi-finals.
However, both clubs have struggled to keep pace domestically and abroad, Milan last featuring in the Champions League in 2013-14 while Inter's most recent appearance came two years prior.
The failure of the national team to reach next year's World Cup was a hammer blow to the Italian game, and Messi believes the two Milan rivals returning to European football's top table would go some way to repairing the damage.
"Italian football in recent years is no longer the same. And I believe that this has to do not only with the non-qualification to the World Cup," Messi said, in quotes reported by La Gazzetta dello Sport.
"For example, two greats in Serie A, Milan and Inter, are no longer those that were about 10 years ago and no longer play in the Champions League, and this affects all Italian football.
"They are basically trying to get back, especially the two Milanese clubs must return to be competitive at European level."
Messi was speaking after picking up the Golden Shoe award for finishing 2016-17 as Europe's top scorer. Friday's ceremony marked the fourth time the Argentinian has claimed the prize, equalling Cristiano Ronaldo's tally.