The Blancos could lose Gonzalo Higuain in the coming weeks and have apparently identified the former Espanyol forward as an ideal replacement for the Argentina international.
Real Madrid are reportedly set to offer €10 million plus Fernando Gago for Roma striker Pablo Osvaldo.
Madrid and Roma are set to meet next week to discuss the proposed transfer and, according to La Gazzetta dello Sport, the Blancos will raise the idea of giving Roma Gago and €10m for Osvaldo.
The once-capped Italy international was the Giallorossi's top scorer last season, netting 11 times in 26 appearances in Serie A, but Osvaldo has had his disciplinary problems in the Italian capital and was involved in a dressing-room bust-up with team-mate Erik Lamela in November.
Madrid, meanwhile, are currently trying to persuade Gonzalo Higuain to remain at the Santiago Bernabeu but the Argentina forward has been heavily linked with Paris Saint-Germain in recent weeks, meaning the Liga champions could soon be in need of another striker.