The Mexican striker added to his tally for the season with a 12th goal at Bournemouth on Saturday.
His penalty earned Wolves a 1-1 draw at the Vitality Stadium in a feisty and controversial encounter.
Jimenez is on loan for the season from Benfica and Wolves have an option to sign him for around £30million in the summer.
Coady said: "He's been huge for us. He's a brilliant footballer and at the same time he's a fantastic person, he's fitted into the changing room seamlessly.
"He's come and you'd think he'd been here for years, you really would. He's a fantastic character to have around and you see how confident he is on the pitch at the minute, it's an absolute pleasure to play with him. Long may it continue for Wolves. We want to keep him here for many, many years.
"The decision's up to him and the two clubs but he's a fantastic footballer and a pleasure to have at this club.
"You've got to be (on at him to stay)! It's his decision at the end of the day.
"The two clubs will come to a decision, we want him here."
Wolves face Coady's old club Huddersfield Town tomorrow, with the rock-bottom Terriers having not won since beating Wolves 2-0 at Molineux in November.
"We need to make sure we're ready for Tuesday, look at Huddersfield and their strengths and make sure we're prepared," Coady said.
"What Huddersfield have done in the past couple of years has been remarkable. They were good on that day but we were poor and we've learned from our mistakes.
"We're in a good run of form and we want to keep it going."
After tomorrow Wolves only have two more games before their mouthwatering FA Cup quarter final against Manchester United.
"You look at the draw and it doesn't get much bigger," Coady added. "Molineux will be rocking won't it?! That game under the lights on a Saturday night.
"We can't wait for it but there are some big games before that which we need to make sure we're ready for."