Bale will leave the Spanish giants after nine illustrious years at the Santiago Bernabeu where he picked up five Champions League medals and three La Liga titles.
The 32-year-old has not yet chosen his next destination but Saunders believes a move to the north east would represent a smart choice for the Wales international.
"If I could pick a club for him to go to now, I'd say sign for Newcastle," Saunders told talkSPORT.
"They've got a project; they're going in the right direction - he would slot in.
"The fans right now in Newcastle, because I've been there and I worked there - and I realise how much they love the club - right now they could sell 80,000 season tickets."
Bale was linked with a move to Tyneside in the January window but the player had no plans to leave Madrid mid-season whilst Newcastle put their efforts into bolstering their defence ahead of a successful relegation battle.
Newcastle will look to kick on next season and have already added Matt Target on a permanent deal while looking to tie up the signings of Lille's Sven Botman and young Reims striker Hugo Ekitike.
But a possible acquisition of Bale would represent a first big-name signing since the Saudi-backed takeover of the club last October.
Bale was linked with a move to Madrid-based club Getafe in recent weeks, although this was refuted
Meanwhile, a move to hometown club Cardiff City has also been mooted but nothing has materialised so far.
The Wales forward will want to secure his future arrangements soon, after leading his country to their first World Cup appearance since 1958.
Wales beat Ukraine 1-0 earlier this month to qualify for the tournament in Qatar in November and Bale will want to ensure he is playing regular, competitive football to give himself the best chance of being in optimum shape for the finals.