The 16-year-old spent last term with the Scottish club and is in talks with them regarding a new contract.
The tenacious midfielder could sign and then join up with Burnley's under-23 team for the coming season.
Given the COVID-19 pandemic, Armstrong had limited chances to impress with Motherwell in age-group football last term.
Speaking to the Daily Record, Armstrong's dad Craig said: "His agent phoned and asked if Johnny would be interested in going on-trial at Burnley and it was a no-brainer. They phoned us to say that they wanted him to come for an initial two-week trial.
"After that, Burnley are going on a Scottish tour and they said if he does well then he will be part of their development squad for that trip.
"They've been phenomenal. They've put us up in hotels, paid for all our meals and you couldn't ask them for anything more.
"He will go down for a week then come home before going back down for another week.
"They've said that they'd offer him a scholarship programme, if they like him, because they can't sign him professionally until he's 17-years-old.
"It's an unbelievable opportunity to go and impress at an English Premier League side.
"They told me that they've identified Johnny as a hard-hitting central midfielder with incredible determination."
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