Hodgson – who is taking charge of his 300th Premier League game against Chelsea on Saturday – said he always expected Frank Lampard would make a good manager.
Hodgson, 72, worked with Lampard during his time with England, and will now go head-to-head with the former midfielder in the dugout at Stamford Bridge on Saturday.
The 41-year-old has impressed during his first steps into coaching, having taken Derby to the Championship play-off final last season before returning to Chelsea in the summer.
“Frank Lampard has done a very good job, there is no question about that,” Hodgson said.
“The club have (also) done a good job in encouraging the manager and his staff to blood some of the players that had previously been out on loan. Everyone at the club deserves a pat on the back for that,”
“I’m certain that Frank will be more than happy with how the team has started, the way the team has played and where they find themselves both in the Premier League and the Champions League. It is happy days for him I am sure.”
Hodgson added: “I always had a lot of respect for Frank as a player and I am pretty certain he will make sure the football world has equal respect for him as a manager the longer his career goes on.”
Lampard’s strong start to his new role comes as no surprise to Hodgson, along with that of former England captain Steven Gerrard at Rangers.
Hodgson feels both men have the potential to one day take on the national job.
“When he (Lampard) and Steven Gerrard went into management I had no doubt that they would succeed,” the Palace boss said at a press conference.
“For me it was a question of whether they would go to a club that would give them a chance to really show their great management material and are more than capable of doing the job.”
On the prospects of a future role with the Three Lions, Hodgson said: “They have both been great fantastic servants for England, earning 100 caps – and that is not a bad thing to have on your CV if you want to be an England manager.”