Inniss, a 6ft 5in central defender, impressed during his month-long loan spell with Rob Page’s team this campaign.
Vale won four games out of five games when the 19-year-old was in the side before his season was ended by an ankle injury in the 3-2 victory at Coventry on March 7. After his departure, the Valiants lost their next six matches.
Page wants to bring in four or five new players over the summer, and a loan for Inniss is high on his list of priorities.
“We have spoken to Palace and that is something the lad himself is keen to do,” the Vale boss told The Sentinel.
“We are keen to do it so I think within the next couple of weeks we will have more news. But it is an obvious one because all the supporters know the impact he had when he came into the club.”
Page has made room for a centre-half in his squad by releasing Chris Robertson.