The Ibrox club have already had three bids thrown out, with the most recent offer believed to be in the region of £600,000 with a
staggered payment plan.
Hearts are holding out for a cool £1m for the contract rebel, who has turned down an extension to his current deal which expires next summer.
Head coach Ian Cathro recently declared the matter closed and insisted that Walker would be a pivotal part of his side for the coming campaign, forming part of a formidable attacking trio with Isma Goncalves and Kyle Lafferty.
That was music to Cowie’s ears but, should the time come when Walker does move on, he sees no reason why his ambition should be solely set for Glasgow.
After watching Walker dazzle against Newcastle on Friday night, Cowie said: “The only thing that surprises me is that there only seems to be one team that wants him. On the pitch with him against Newcastle on Friday night – a massive club with players who have a little bit of everything – he proved that he has that X-factor.
“When you train with him on a daily basis, it’s an eye-opener. You see the end product, the goals, the technique. There aren’t many
players like him, especially in Scotland.
“I’ve told him that. He has real quality – something special – and if he really wants it then anything can happen in his career, whether that is moving to a bigger club or international honours.
“It’s all there for him. What he needs to do is be consistent and get his head down.
“He has the quality that can take teams places and, from a selfish point of view, I hope he does it for us, but if someone is willing to pay the money that this club values Jamie at, then so be it – I’ll wish him well.”
Walker has been one of Hearts’ standouts in pre-season, shunning the speculation over his future to turn in superb displays against Linfield and Newcastle. He found the net in both encounters, and claimed man of the match in the 2-1 defeat to the Toon.
Walker’s form has calmed any suggestions that a desire to move on would affect his performances, and he is set to play a starring role when the Tynecastle outfit’s season officially begins against Elgin City tomorrow.
And Cowie has joked that he should take the credit after a week of canvassing the 24-year-old in Ireland.
“Well, this is just what happens when he spends a pre-season trip rooming with me,” smiled the former Scotland ace. “I’ve managed to get inside that head of his! Although, he’s a rubbish roommate – I have to do all the talking.”
Joking aside, the time spent in the Emerald Isle has offered Cowie an insight to Walker’s predicament.
He continued: “His mindset is that of a player who is dealing with something that he has never experienced before; everything that happened at the start of the close season. It’s difficult for him.
“This is the first time Jamie has really gone through all this transfer interest and being the centre of all this publicity. That can be difficult for anyone to go through. But, I’ve said to him many times, his future really will take care of itself.”