It looks a straight shoot-out between the Southampton teenager and the experienced Chelsea defender for the 23-man squad heading to Brazil, as Everton left-back Leighton Baines appears all but assured to be included.
Shaw made his England debut as a half-time replacement for boyhood idol Cole in Wednesday's 1-0 defeat of Denmark, putting in an impressive display before returning to club matters this weekend.
The 18-year-old produced another sturdy performance in Saints' 1-0 win at Crystal Palace, after which he revealed Hodgson had spoken to him about the Cole comparisons.
"I try to ignore that sort of stuff, the media attention, as obviously it is going to happen," Shaw said.
"I spoke with Roy about it and he said that 'there is nothing you can do about it, this stuff is going to happen'.
"I am going to keep pushing myself and see what happens at the end of the season.
"I am not thinking about Brazil at all. I've still got nine other games left and I will focus on them and see what happens at the end of the season."
Shaw was one four Southampton players in Hodgson's 30-man squad to face Denmark, joining the previously-capped Adam Lallana, Rickie Lambert and Jay Rodriguez.
That was a record number of call-ups for Saints, but Shaw believes that number could soon be beaten as the likes of Nathaniel Clyne, Calum Chambers, Jack Cork and James Ward-Prowse look to follow suit.
"It is unbelievable [to be at a club with so many Englishmen]," he said.
"There were four of us in the England squad on Wednesday and I am sure there is going to be more in the future.
"The team spirit is great, especially when we are winning. It is very high and it is like a family club.
"Everyone looks after each other, especially the older lads with the likes of me, Calum and Prowsey. They help us a lot at training."
Saturday's match at Selhurst Park gave ninth-placed Southampton an 11-point cushion over nearest rivals West Ham, while it saw Palace slip closer to the drop zone.
Cardiff's 3-1 victory against fellow strugglers Fulham cut the gap to two points ahead of Palace's back-to-back trips to the north east.
Sunderland await next weekend before they then take on Newcastle - matches during which Eagles boss Tony Pulis knows his side need to show mental strength.
"The most important thing is that you stay really focused," he said.
"The lads are very, very disappointed because they've worked very hard and got nothing out of it, but that's the Premier League for you.
"They've got to understand there is quality in every team you play and you have to really be on your mettle - you've got to concentrate for 90 minutes to get those results."