The Finnish frontman is on trial with Ole Gunnar Solskjaer's club and scored in Friday's pre-season friendly with their Norwegian rivals Brann in southern Spain.
Dalla Valle is keen to get a new experience and could end up playing Champions League football at Molde before he eventually returns to Craven Cottage.
The 21-year-old has made just two substitute appearances for Fulham since his switch from Liverpool in 2010 as part of the deal that took Paul Konchesky to Anfield, spending spells out on loan at Bournemouth, Dundee United, Exeter and Crewe.
"He wanted to play in Holland or Norway, so that's why he's at Molde on trial with view to a loan move," said Fulham boss Martin Jol.
"He's a young player who is learning his trade. He did well at Crewe, which gave everyone confidence again."
Fulham last week