The Reds head into Wednesday night's game at Wigan looking for a fourth successive Premier League victory, with confidence soaring after the 2-0 win over leaders Chelsea on Sunday.
They are only five points off fourth place which is currently occupied by Manchester City.
With a run of games between now and the turn of the year against teams currently below Roberto Mancini's side, there is a real chance to build some momentum and restore the damage done by a poor start to the season.
However, unlike predecessor Rafael Benitez, Hodgson will not be "guaranteeing" a top-four place.
"I don't wish to play down our chances but I think it is unfair to ask coaches like myself, who have had a bad start to the season and fallen way behind, whether they will be in the top four," he said.
"My answer will only set me up for ridicule later on. I would like to really discuss our top-four potential when we can really see whether it is a truly viable proposition or not.
"I'll keep my powder dry and you can happily question me with six games to go and I'll give you the intelligent answer.
"It is all to play for at the moment and I certainly wouldn't write us off that's for sure but, on the other hand, being five points adrift is clearly not where people want to be."
Although he is reluctant to say it outright, Hodgson believes his team have turned a corner after a disappointing start saw them take just six points from their first eight matches and drop into the bottom three.
He knows this is a crucial period to regain lost ground, but is acutely aware the winning run could end as quickly as it began.
"Everyone is working hard to make sure we try to become a better team, not just a group of talented individuals, because in this league you need that," added the 63-year-old.
"The mindset has always been there. We had a bad start and things weren't going our way and we were a little bit unlucky in one or two games.
"If you analyse the games we have lost they have mostly been against teams away from home who are capable of beating anyone - Manchester United, Manchester City and Everton in the derby.
"We have always had the feeling if we can get our players fit and we can get our best players out there we are capable of giving teams a very good game.
"We don't have any fears in that respect, but we have a relative degree of modesty because we know unless we produce the right performances and get ourselves going in every game from start to finish, we can drop points where we shouldn't drop them.
"Steven Gerrard has said to me on many occasions that getting through this period and then getting some good results will make us stronger because we will never forget the bad period we have had.
"But we will always be anxious it might reappear."
Defenders Glen Johnson (groin) and Fabio Aurelio (Achilles) return to the squad but Sotirios Krygiakos (tonsilitis) and Joe Cole (hamstring) miss out.