Jones, who played with Wise at Chelsea and Wimbledon, spent 18 months at Elland Road between June 1989 and November 1990 and believes the 39-year-old can achieve success in West Yorkshire.
"I spoke to Dennis on Monday night. I told him what a brilliant city Leeds is and what a good move it would be if he can get the fans back and working with Ken Bates is a great combination," Jones told Yorkshire Radio.
"This is the next step for Dennis after Swindon."
Wise is set to be unveiled today after his appointment was confirmed on Tuesday when Leeds finally agreed terms with Swindon over the former England midfielder.
Jones also revealed he will be returning to Elland Road to give Wise his full support, saying: "I will come back without a doubt now.
"I told Ken (Bates) I'd love to come back when I get the chance. Leeds fans gave me so much and it's a club very close to my heart. Fingers crossed it will be the same for Dennis."