Former Manchester United and Arsenal forward Welbeck provided Watford with a boost this week following his return to training.
The 29-year-old joined the Hornets on a free transfer from the Gunners last summer, but he has featured in just five Premier League matches after sustaining a hamstring injury in October.
Second-bottom Watford, who are two points adrift of safety, have the worst scoring record in the top flight, with just 17 goals from their opening 21 games.
Creative midfielder Cleverley has also been out since October with a foot injury.
"Danny is back out on the grass so he is making good progress," said Pearson. "Cleverley is still a while away. I don't want to put a time frame on that. When he is back, I want him back for good.
"I don't want to put players at risk just for the sake of another couple of weeks. I want to make sure they are absolutely right."
Watford's campaign has been blighted by a host of injuries and Pearson confirmed the impressive Kiko Femenia will miss his side's trip to Bournemouth this weekend as he battles a hamstring issue.
Sebastian Prodl and Daryl Janmaat remain long-term absentees, but Craig Cathcart is available.
As for the Cherries, Eddie Howe's squad continue to be riddled with injuries and once again have a host of absentees.
Josh King, Adam Smith, David Brooks, Nathan Ake, Charlie Daniels, Lloyd Kelly, Jack Stacey and Arnaut Groeneveld are all sidelined.
The Cherries sit down in 18th place in the Premier League, just one place and one point above their opponents this weekend at the Vitality Stadium.