Ameobi, 33, is best known for his time at Newcastle, where he scored 79 goals in 397 games in a lengthy spell, but ended last term at Crystal Palace under his former Magpies boss Alan Pardew, only to be released this summer.
Since then, the Nigerian international has been without a club, and nearly two months in to the season, Ameobi remains a free agent despite links with a number of Championship clubs.
The Sun report that he couldn't agree a deal with Huddersfield Town and was snubbed by Wolverhampton Wanderers, with Sheffield Wednesday now a potential destination.
The Owls remain in the market for a striker even after signing Lucas Joao and Fernando Forestieri over the summer, and it now seems that Ameobi could be a target.
It's stated by The Sun that Ameobi hopes to win a deal with Wednesday during a proposed trial spell with the club over the coming week, as manager Carlos Carvalhal runs the rule over the veteran striker.
With strength and aerial ability, Ameobi would offer a veteran, experienced presence in attack for Wednesday, and a potentially ideal mentor for the raw buy physically gifted Lucas Joao - and whilst the loan window remains a possibility for Wednesday, the idea of signing Ameobi on a free transfer seems to have been floated at Hillsbrough ahead of his trial period.