Hammers manager Sam Allardyce has been tipped to leave Upton Park after the last game of the season against Newcastle United on Sunday.
But another name which has also been consistently mentioned is that of South American tactician Bielsa, the current Marseille boss.
The former Argentina and Chile coach is something of a footballing eccentric and is famous for deploying a 3-3-3-1 formation with an aggressive pressing style.
And he has done enough to impress Sullivan junior, who often uses the social media network to tweet out club news on his dad's behalf, after he praised the 59-year-old on Wednesday night.
Responding to a fan who was urging the club not to go after the maverick boss, Sullivan said: "Bielsa is a great manger in my opinion done very well at Marseille!"
@ArchiAAL belisa is a great manger in my options don't very well at Marseille!!— Jack Sullivan (@jsullivanwhu) May 20, 2015
But after the tweet was highlighted by other fans as a potential hint as to who might replace Allardyce this summer, Sullivan moved quickly to pour cold water on the rumour mill, insisting he was just speaking his mind.
The youngster simply added: "Don't read into it. My opinion."
So has Bielsa done as well as young Jack believes?
He has led Marseille to fourth in Ligue 1 so far this season, with an outside chance of qualifying for the Champions League.
They must beat mid-table Bastia in their last game and hope third-placed Monaco somehow fail to beat lowly Lorient to stand any chance.
His future in France is unclear and he recently said he is still waiting to see if he will be offered a contract for next season.
His stats are pretty impressive, though. He boasts a winning percentage of 48.58 in his career so far, with 137 victories taken from 282 games as a manager.
While some fans are eager for a different approach and style to what Allardyce brings to East London, some feel Bielsa is perhaps too much of an extreme change.
Known as a strict disciplinarian, his preference for all out attack has endeared him to Marseille fans, but he has also been criticised at times for being too inflexible and naive.