Jose Mourinho's men had to settle for second spot in La Liga last term, but they currently top the Primera Division table and hold a one-point lead over Barcelona.
And Messi feels that Madrid's improvement is partially down to their summer transfer activity, and he has also stated that they have grown as a team.
"Real Madrid have strengthened their team pretty well in the summer. They intended to do better than last term and have been doing just that," Messi was quoted as saying by Marca.
"They have grown a lot since August and are a better team than last season."
Nevertheless, Messi then insisted that Barcelona have made similar steps forward.
"However, we have also strengthened in the summer and have improved as well."
Barcelona are currently preparing for the league match away against Athletic Bilbao on Sunday.
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