Gerrard may receive some advice from his two managers on the issue, but it will be ultimately be up to the midfielder.
It is thought that Gerrard was expected to announce his retirement after the Three Lions' participation in Brazil at the age of 34 in order to prolong his career at club level with Liverpool.
Thompson also praised the longevity of the Liverpool talisman when he appeared on Sky Sports earlier.
He said: “Steven knows that he’s got Champions League football and Premier League football and that is most difficult. He’s 34-years-of-age and he wants to prolong it.
“Brendan will just say: ‘Steven, you think about it. Go away and have your holiday with your family, discuss it with as many members of your family as you want and you make the decision when you feel ready to actually announce it.’”
"At 34-years-of-age he has done wonderful to stay there, but if I was looking at it, having the Champions League and the Premier League to go for, it might be the time where he thinks ‘if I want to prolong my career and play as long as I can I might need to do that. I might need to step aside’.
“Yes, it may be doing it for England and it may be doing it for Liverpool but it’s for him that he must decide.”
In the early part of his career, Gerrard did have some injury struggles but has been representing England for the best part of a decade, and been a regular under four different managers.
Avid Liverpool fans will want Gerrard to retire from international football in order for his concentration to be solely on helping Liverpool achieve success both at home and in Europe, whilst some have viewed him as a bit of a scapegoat for England's poor showing in Brazil, which has seen them eliminated at the group stages for the first time since the 1950s.
Roy Hodgson will want Gerrard to continue as England captain for the qualifiers for Euro 2016 and Thompson suggested that may be because he is still one of the country's best midfield players - but it could also be because Gerrard is the most natural holding midfield player at England's disposal given where he plays for Liverpool.
Brendan Rodgers has always said it would be up to Gerrard, and one would expect that to be the case, but with Liverpool now showing signs they could be a force again, if the Liverpool captain thinks it will be to both his and the club's advantage if he decides not to continue playing for his country, then that is a sacrifice he could be willing to make.