Mario Balotelli's agent Mino Raiola has revealed that the striker will not be leaving Anfield this summer.
Graham Dorrans has signed a two-year deal with Norwich City following a successful loan spell with the club.
As Taylor pointed out, Hodgson was not the popular choice to succeed Fabio Capello.
Former England boss Taylor believes there are still some within the media who would have preferred Harry Redknapp to get the job.
However, he feels the Football Association got the right man and believes the England team are benefitting from Hodgson's involvement.
"Roy has done well," Taylor told BBC Radio 5 Live's Sportsweek programme.
"There was a section of the media who wanted Harry Redknapp and he has not yet overcome the fact he wasn't neccessarily the first choice for everybody.
"But it has worked well.
"This is Roy. He is not flamboyant. He doesn't speak in headlines. That bristles certain people. He had a reputation of being cautious.
"But whatever people think about him, he is the only England manager to be appointed with previous international experience.
"He has been there. He has seen it. His experience of international football before he got the England job is a great plus."
Le Saux played for Hodgson during his final days at Blackburn.
And he recalls an honesty about the 66-year-old that brought out the best in players.
"He has an honesty and professionalism about him," said Le Saux.
"He respects people and therefore gains respect from them.
"Players need to look at their manager and say I want to work for you. He has that quality."
As Taylor knows only too well after failing to guide England to the 1994 World Cup, the price of Hodgson not succeeding in booking a place at next summer's World Cup Finals in Brazil is likely to be a heavy one.
It should not come to that though.
Both Taylor and Le Saux expect England to get the win they need against Poland at Wembley on Tuesday to confirm automatic qualification without taking the hazardous play-off path.
Team selection will be crucial, with most observers anticipating changes to the side that beat Montenegro on Friday will be kept to a minimum for a match when Tottenham defender Kyle Walker will be suspended.
That means keeping faith with Andros Townsend, who was so electrifying on his debut at Wembley but whom, as Taylor has seen, might not always reach such an impressively high level.
"Andros went out on loan nine times to nine different clubs," said Taylor.
"He was at Watford and the performances I saw there were completely different from the performance I saw the other day, when he was first class in his directness.
"People will be aware of that.
"It will be very interesting to see whether the opponents already recognise this player can be a threat and try to stop him.
"We will see how he handles that situation."