Tonne, 21 has made just one start for the Bramall Lane club but in his further six substitute appearances netted twice in fixtures last season at Burton Albion (2-1) in the Johnstone's Paint Trophy and at home to Bury (4-0).
The Norwegian national is due to take part in a trial in his homeland who currently play in the First Division, it is expected that he could join the club on loan but not in a permanent move. He is contracted with the Bramall Lane club until June 2014.
The HamKam.No website said; "The 21-year-old winger Erik Tonne is coming over from Sheffield United to audition.He signed an extension with Sheffield in 2012 until the summer of 2014, so it will only be a matter of a loan if a move is discussed."