The Cottagers were struggling in the relegation zone when Hodgson was appointed manager in December 2007, but after keeping the club up in his first season, the former Blackburn and Inter Milan boss led them to seventh place and qualification for Europe in the following campaign.
Fulham are currently 10th in the table and have made it to the knockout stages of the Europa League, with Hodgson signing a new 12-month rolling contract in December.
But the 62-year-old, who has international managerial experience with Switzerland and Finland, has frequently been touted as a successor to Capello when the Italian's time in charge of England comes to an end, and Laws believes Hodgson has the ideal credentials.
'He's very experienced, he knows the game inside out and I think he'd be the perfect choice,' said Laws. 'I don't think you can be England manager without all those ingredients. You have to have had those experiences and I think you have to be at a certain age. It's not one for a young manager; I think you have got to be seasoned. You need that aura about you and he has certainly got that.'