Following a 13-game winless run, Palace decided to sack Patrick Vieira last month and reappoint Hodgson, who previously managed the club for four years between 2017 and 2021.
The Eagles were just three points clear of the drop zone when Hodgson took over, but he has overseen an upturn in fortunes since his arrival.
Palace picked up 10 points from Hodgson's first four games in charge before they suffered the first defeat of his second spell against Wolverhampton Wanderers on Tuesday.
After losing 2-0 to Wolves, the Eagles bounced back on Saturday lunchtime, prevailing in a seven-goal thriller against West Ham United at Selhurst Park.
Jordan Ayew, Wilfried Zaha, Jeffrey Schlupp and Eberechi Eze all got on the scoresheet to guide Palace to a 4-3 victory that secured their Premier League safety.
Hodgson only has a contract with Palace until the end of the season, and he refused to comment on whether the club's impressive form under his watch would lead to him extending his stay.
"I'm not prepared to talk about that at all," Hodgson told reporters following the win over West Ham.
"What happens after the season will happen. At the moment, I shall enjoy this last month and I'll make no comments whatsoever.
"It's kind of you to ask the question but I prefer to say nothing. Otherwise I'll come to James Tomkins' amusing comment of: 'What are you looking for? Another gold watch?' - which I'm not!"
After guiding the Eagles to the 40-point mark with four games to spare, Hodgson conceded that he was surprised by how quickly his side have moved away from danger.
"I suppose I'm surprised because I didn't know the players," the Palace boss added. "If I had known the quality there was here to work with then perhaps I wouldn't have been quite so surprised, but I had to find that out."
Palace currently occupy 11th place in the Premier League table, and if they can hold on to their current position, it would represent their best finish since the 2017-18 campaign.
The Eagles will face Tottenham Hotspur next weekend before they round off the season with games against Bournemouth, Fulham and Nottingham Forest.