It's been reported the ex-Belgium captain has been considered as a replacement his former boss Roberto Martinez following his departure.
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However Jordan has warned the Clarets boss not to take the risk as the role could be a 'poisoned chalice'.
Kompany took the job at Turf Moor last summer and and replaced long-standing boss Sean Dyche, who had got the Clarets promoted to the Premier League in 2016.
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The former centre-back had been managing Belgian side Anderlecht - the club he began his footballing career with - but was swayed to join relegated Burnley and attempt to win them promotion back into the Premier League.
Although it only began in 2020, Jordan thinks Kompany's managerial career - alongside his time as captain of Belgium and Manchester City - shows he won't be the type to jump ship at Burnley.
And he thinks Kompany has a great chance at becoming a Premier League manager if he sticks at it at Turf Moor, with the Clarets currently sitting top of the Championship and in pole position to go up.
"He's a leader and I think leaders have more substance than followers," Jordan told talkSPORT. "So he doesn't strike me as someone that would jump into a job and then jump out of it when he felt something immediately better came along.
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"He stayed at Anderlecht for three years, I think he did a job, you [co-host Jim White] questioned if he did a good job at Anderlecht.
"He's at Burnley doing a good job at getting them together and changing the brand of football they play alongside potentially getting them out of this division at the first knockings."
Jordan then went on to explain that it's not just his good position at Turf Moor that should persuade him to stay, but the chaos that's going on amongst Belgium's national team set up, too.
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After crashing out of the 2022 World Cup in the group stages - despite their team being regarded as a 'golden generation' - the Belgian FA announced it was agreed prior to the tournament Martinez would leave after Qatar.
All this followed a series of reports suggesting unrest within the Belgian dressing room.
Meanwhile, players such as ex-Chelsea star Eden Hazard and Manchester City's Kevin De Bruyne were not up to their usual standards in the group games.
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And Jordan thinks it would be a risk for Kompany to jump into what looks like a troubled national team side when the 36-year-old is at the peak of his development - even if though he led them as captain 36 times before his retirement in 2020.
"The Belgium job could be a poison chalice, because what's coming behind this so-called 'golden generation'?" Jordan asked.
He continued: "He's at a stage where he's developing his managerial career, he's still very young in managerial terms.
"He's got an opportunity to manage in the Premier League rather than do a part-time job as an international manager in a national that's underachieved in the last six years with its best generation of footballers.
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"I think it's degrees of loss, potentially leaving a decent Premier League job, potentially if he gets Burnley there, to earn a job at a stage of his career when it's perhaps for a slightly older manager at a different time in their career.
"That's not suggesting Roberto Martinez was particularly old when he took the job because he wasn't."
That being said, Jordan does think Kompany has a right to move on from Burnley when the situation - unlike the potential one with Belgium - is right.
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He added: "I don't think it would be the right move for Vincent Kompany, but I'm not suggesting all roads lead to Burnley and to stay at Burnley."