Hodgson only penned a one-and-a-half year contract when he joined in February and his current deal is set to expire in June.
"He's massively important to the club," Jones told the Sunday Mercury. "He proved that last season with the situation West Brom were in before he arrived. He came in and pretty much made the difference of keeping the team up.
"The direction and the organisation he brought to the team set them on that great run and I'm sure we will show that again for him this year.
"The aim of the gaffer and the whole club in general is to take the club on to the next level. We all want to get rid of that ('yo-yo') tag and become an established Premier League team looking up and onwards.
''That's definitely the plan from the team at the moment and the whole club in general to keep on pushing on upwards and improving."