Hathurusingha flew back to Bangladesh on Wednesday after a vacation. He spoke to reporters at the BCB building on Thursday, reports bdnews24.com.
"Bangladesh cricket will benefit if Mustafizur develops quickly and performs well. So if it does not harm his health, I think it is a good thing for him to go and play," the Sri Lankan coach said.
Having returned from Indian Premier League after helping Sunrisers Hyderabad win their maiden crown, the 20-year-old seamer is currently in his hometown Satkhira.
Speculation is swirling over Mustafizur's visit to England after he received an injury ahead of the second qualifier in the lucrative T20 tournament.
Following an initial assessment of his injury, Bangladesh Cricket Board physiotherapists and doctors said a decision on Mustafizur's visit to England would be made taking his physical condition into account.
Bangladesh will play in the Champions Trophy in England next year. Hathurusingha thinks Mustafizur's county experience there will help him prepare for the One-Day tournament.
"If you want to improve performance, you have to play in England's conditions. You don't go there, you don't know," Hathurusingha said.
"It is a rare opportunity for Bangladesh players to play there. If I can send four players I will send them all. It is the best way to do it."
Sussex signed Mustafizur for this season's NatWest T20 Blast and Royal London One-Day Cup. They hope to get the young left-arm seamer for the match against Kent on Jun 10 in their backyard, Hove.
The BCB is yet to officially say anything on the matter though different sources indicate that Mustafizur is having some difficulty with his hamstring. But it is not serious enough to stop him from playing.
Mustafizur, however, have told his close acquaintances that although his body may recover, he is mentally tired after having played without a break for a long time.
Mustafizur's spectacular success in limited-overs cricket has shifted the focus away from his promising possibilities in Test cricket, but Hathurusingha has started thinking about it.
The youngster was handed his first Test cap against South Africa last July. He was adjudged Man-of-the-Match after taking four wickets on the rain-marred debut but could not bowl a single delivery in the next match which was washed out.
Bangladesh are yet to play a Test after that, but in the meantime, Mustafizur's consistent success in one-dayers and Twenty20s has been impressive.
Bangladesh have quite a number of Tests lined for the next few years - both home and abroad. Hathurusingha thinks keeping Mustafizur fit will be the biggest challenge.
"He has played two Test matches and had become Man-of-the-match in one with four wickets. At the start it is impressive but... it is going to be a challenge - he has to be fit, we have to look after him," the coach said.
Mustafizur complements his slowers, cutters and inch-perfect yorkers well with a delicate change in action and a snapping wrist motion to give any world-class batsman a hard time at the crease.
But Hathurusingha feels batsmen will eventually find a way to deal with his box of tricks.
"We all know that his mystery is going to be found out very soon, so at the same time I am looking forward to his intelligent cricket," Hathurusingha said.
"So we will find ways for him to be competitive. Our challenge is to look after him, develop him and keep him in the pack to play for Bangladesh."
Bangladesh are scheduled for three Tests this year and at least eight more in the next.