Moussi, who last played professionally for HJK Helsinki three years ago, tweeted a picture of the pair together at Leeds' Thorp Arch training centre.
In it, Bamford is seen handing over a shirt of his, complete with the message: 'To My Bro The Moose, My First Roomy! Best Wishes'.
While Moussi's tweet reads: 'One more to the collection. #DontWorryIWillBringHimBackHomeLol #Nffc'
Bamford, who moved to Leeds for around £7 million in the summer, is expected to spend the rest of 2018 out injured - and could miss both the Whites' fixtures against Nottingham Forest.
The 25-year-old left Forest for Chelsea in 2012 but moved to Middlesbrough in January last year after failing to break into the Blues' first-team plans.
Moussi was released by Nottingham Forest two years after Bamford's exit and later appeared for Leeds' Saturday opponents Birmingham City before ending his career in Finland.
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