Barkley, 23, is preparing to leave Merseyside this summer after rejecting fresh terms at his boyhood club, but Koeman revealed on Wednesday (26 July) that there are no offers on the table for the playmaker at present.
Everton valued Barkley at £50m earlier this year but Tottenham are hoping to strike a deal worth around £25m for the playmaker, who has just one year left on his deal at Goodison Park.
Tottenham manager Mauricio Pochettino has garnered a reputation for developing young talent in north London, and Barkley is seemingly keen to join the Argentine and attempt to displace the likes of Dele Alli and Christian Eriksen in Tottenham's starting line-up.
A number of the Premier League's fabled 'top six' clubs have also glanced in Barkley's direction. But Collins, who spent two years at Goodison Park, expressed his doubts over Barkley's work rate and attitude and believes his prospective new manager will have a tough time trying to light a fire within him.
"Some managers, you look at him and you say he's got talent, can I put that desire and that work ethic into him and turn him into a top player," Collins told talkSPORT. "But it's difficult to give players that desire. When I watch him sometimes he doesn't really want the ball all the time."
"Is it confidence? I don't think so because he's got a lot of talent, he's got skill, he's got power, he's got speed but to be a top player – as we are all talking about it – you have got to have the whole package. At this moment when I am seeing him he doesn't have the whole package."
Everton's proactive attitude in the transfer window has softened the blow of Barkley's impending exit. Koeman has strengthened the Toffees' senior squad with seven senior players, and Collins thinks the re-signing of Wayne Rooney all but ended Barkley's career at Everton.
"I think Wayne Rooney is a replacement for Ross Barkley – I think they are probably playing a similar position," Collins added." When they signed Wayne Rooney I thought the writing was on the wall for Ross Barkley.
"He's talented, he's got skill, he can beat a man and he can shoot but end product – 21 goals in 150 matches – I don't think it's a great figure. Sometimes he doesn't run, work and sweat enough for the team when you watch him. If he had Wayne Rooney's attitude and desire then I would class him as a top player."