Be prepared that they may be initially reluctant about you seeing the children - children in foster care often have a lot of broken relationships and unfortunately extended family can sometimes push for contact because it's their 'right' to see the kids, but then those extended family pop along to see them then leave that visit, to go back to their own lives, leaving the kids a bit bewildered. They might not have a great understanding of who you are at this point, depending on their ages and that you were limited in how much mum let you see them.
I would think very carefully about what you think you could offer to the children and commit to and then approach social services in the area they are living , if you know it (no point going to your local area, if they have no involvement with the family) Contact the safeguarding hub/mash/single access point, explain who you are and that you believe the children have a social worker and ask for your details to be passed on. You might have to be a little persistent, social workers are stupidly overworked, it's not personal if they don't call you back first time.
Social workers (and foster carers) are usually supportive if you can show that you are doing it for the benefit of the child, and that you are willing to be consistent. Eg would you be ok with sharing information about their dad, photos, what he was like etc, even if they weren't ready to see you? Would you be willing to meet up for short visits regularly to build their trust? Would you be prepared if the children only wanted to see you with their foster carer, or only some of the children wanted to see you?
I have worked with children where extended family wanted to get involved but expected the children to behave as though nothing had happened - that they should just be ready to be collected by them, go on a day trip no questions asked and be fine with it. Or to go visit dying grandad in hospital, play the dutiful cute grandkid and then be dropped back home. Or would visit the child, promise to visit again and let them down and just ghost. Apologies if I sound cynical, I'm sure you have good intentions and I don't mean to put you off, just for you to be aware why social workers and foster carers can be somewhat protective of children who are in this situation and what you might need to take into consideration. Having supportive, consistent, unconditional relationships is the best thing for any child in care but they sadly often are let down.
You mention things are being made permanent, if so it's unlikely you would be asked at this stage if you wanted to care for them (there is a window during proceedings where those assessments are agreed usually) however you may be asked if you would want to be considered in future, just by prepared to be asked and to say no & why - it's very common for family to wish they could but not actually be able to do so, eg because if the commitments of their own children, not having space, work commitments etc. However that doesn't mean you can't be involved, whether its for visits, trips out, or sleepovers if it were possible.
Good luck with it