Gen Chaisit Shinawatra said on Wednesday that his cousin made the suggestion in a phone call a few days ago.
His advice was reflected in the Pheu Thai Party’s decision to field only his sister Yingluck and brother-in-law Somchai Wongsawat on its party-list for the Feb 2 election.
Gen Chaisit warned protesters not to push Shinawatra family members into a corner by pressuring them to leave the country.
He hoped that army chief Gen Prayuth Chan-ocha would use his connections with protest leader Suthep Thaugsuban to break the political deadlock.
The former army chief and supreme commander, who turned 69 on Wednesday, termed the protests a ''quiet coup'', pointing out that police and soldiers had made no effort to end the month-long rally.
Thaksin has been keeping a low profile since the demonstrations began in late October.