"It is expected that his signing with Real Madrid will be officially announced on Monday," wrote Marca, without citing a source.
Another sport daily, As, also reported that Altintop's deal was nearing completion and said his arrival was "at the express request of (Real coach Jose) Mourinho".
Altintop, currently sidelined with a back problem, has only played 63 games for Bayern in an injury-plagued four-year spell but will arrive on a free transfer because his contract at the German giants is due to expire.
The arrival of 28-year-old Altintop follows that of his 22-year-old international team-mate Nuri Sahin, who completed a 10 million euros ($14m) move to Real from German champions Borussia Dortmund last week.
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