The Saddlers currently have four frontmen on their books in Josh Gordon, Elijah Adebayo, Morgan Ferrier and Mitch Candlin.
But at a fan focus meeting earlier this week, boss Darrell Clarke said he couldn’t guarantee Ferrier would remain at the club – with the 24-year-old having previously expressed a desire to leave.
Clarke has already said he is working to strengthen his frontline before the transfer window closes.
But while Pomlett wants to see additions, he also wants the entire team to start chipping in with goals.
“I agree with the manager that is an area we need to strengthen and I think the fans would agree with that as well,” the chairman said.
“There is the budget for a couple of strikers and we are looking to bring a couple in during the next week or so.
“But let’s be careful about this, we need more goals from the centre-halves, we need more goals from midfield. Walsall had a 20-goal a season striker last season (Andy Cook) and we went down.
“We are looking for more goals from all over the pitch. It’s not as simple as we need a new striker. I agree we do. But what we actually need is goals all over the pitch.
“That is something we didn’t do last season. It’s an overall picture we are looking at.
“Do we need new attackers? Yes, we do. Is there a budget to achieve it? Yes, there is. Will that solve all the problems? No, it won’t. We need to get the midfield and the defenders making a contribution as well.”
Meanwhile, Clarke says his preference is to sign a striker on permanent basis rather then on-loan.
But he says when it comes to goalscorers, you often have to think outside the box.
“We have a long list of targets,” the 41-year-old said.
“Ideally I’d like to get a permanent one.
“But everyone is looking for that 20 man goalscorer and they don’t grow on trees.
“We are not in a position, like most clubs, where we can get that one which guarantees you 20 goals.
“There are very few people that do it, to be honest with you, you are looking outside the box – you are looking for that potential and that desire.”