The former Bees striker has plotted nine wins from 21 matches since taking over until the end of the season and came close to smashing Huddersfield's five-month unbeaten league record.
Forster said: "I think an announcement will be made soon and until then it's hard to plan for anything. But I'd love the job.
"I've been in the game 20 years. In my opinion it's the greatest game in sport and I really want to stay in it.
"I feel honoured to have been given the role in the first place. I think I've learnt a lot and would love to carry on.
"It's been tough at times. We've still got seven players out and that's going to hurt any team. But I can't fault the lads who've been playing."
Source: PA
Source: PA