Paper says Moscow proposed sending jets to protect Syrian president and warned coalition against "getting close".
Al-Diyar, a Lebanese newspaper close to the regime of Assad, said on Monday that Moscow had alerted the US-led coalition not to "get close to Assad's plane in order to avoid an aerial battle".
It is expected that Assad's plane will fly to Iran through Iraqi airspace, al-Diyar reported.
Iran's official news agency, Fars, said on Friday that Assad was expected to visit Iran in late December or early January. Al-Diyar reported that the exact date would not be disclosed, citing Syrian intelligence sources.
The embattled president in October flew to Moscow for a meeting with Russian President Vladimir Putin, in what was believed to be his first foreign trip since the start of an uprising against him in 2011.
Fars said on Sunday that the scheduled trip would come as the Syrian army secured victories against "terrorist groups". Tehran, an ally of Assad, adopts the Syrian regime's language and labels most opposition groups as terrorists.
Russian jets began bombing Syrian opposition targets in September.