The Argentine has been heavily linked with a move away in recent months, with fresh reports popping up on Monday stating Los Blancos were set to make a move.
However Carlos Beto Yaque and Rolando Zarate were seen entering Inter’s offices, with Yaque stating Lautaro won’t be going anywhere.
“It was just a courtesy visit, that’s all,” he told reporters.
“There is nothing with Real Madrid and Barcelona. Lautaro is staying here at Inter.”
Sky Sport Italia reports the two sides will meet once the summer transfer window has ended in order to discuss a new contract.
Lautaro’s current deal has a €111 million release clause that is valid for a few weeks in July, a figure no club was willing to pay this season.
Last season the Argentine netted 20 goals in 49 appearances in all competitions for Inter.