Surprised to read 323s are going; they're not life expired surely!?
Popular rumour is that they will be moving to London Midland to bolster the fleet there, as additional units will be required by them (or the following franchisee) for Chase line electrification and further strengthening of Cross-City services.
The actual story is back in the CP4 HLOS it was proposed all the 323s would go to LM (it wasn't proposed LM would get extra 350s though.) Porterbrook liked that idea and were also aware they would have plenty of off-lease 319s, so they tried to get Northern bidders to take on re-engineered 319s to replace 323s and wanted to be able to offer bidders of the next LM franchise all the 323s. They've succeeded with the latter but failed with the former. It's completely down to Porterbrook that the 323s are leaving Northern.
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It has been stated on here and elsewhere that Porterbrook want to concentrate all their 323's into 1 fleet so they will be heading south to join their mates in the West Midlands.
It's not guaranteed yet. There's nothing to stop bidders of the next LM franchise rejecting using 323s altogether if they come up with a viable alternative.