A 3-2 win over Liverpool at home on Sunday moved West Ham up to third in the Premier League table, just three points shy of league leaders Chelsea at the moment.
After threatening to break into the top four last season, there is a real belief amongst West Ham that they could gate crash the Champions League party at the end of the current campaign.
Sherwood conceded that he expected West Ham to drop off from last season as he felt that they overachieved, but now is the time for the club to provide funds for Moyes in the January window.
He believes there is no reason not to trust the West Ham boss with money in January and feels the club could really get into the Champions League if there is extra investment into the squad.
Sherwood said on Premier League TV after the match with Liverpool: “No one expected them to be third.
“Well I certainly didn’t expect them to emulate what they did last season, I thought it was an overachievement, but perhaps it was not.
“And come January, you saw the Czech investor, he might say you know what let’s kind of spend again as I trust this manager.
“He has been listening to us for years saying that the London Stadium has no atmosphere, but they sounded pretty good there today and the players responded.
“They might spend again, why wouldn’t you trust this man now? I think he has done his rehearsal there.
“Give him the money and see where you end up with that. [Maybe] the Champions League, aim for the stars.”
Moyes has been keen to add a striker to his squad since last January and it remains to be seen if he gets his wish this time around.