Appiah has been a free agent since leaving Fenerbahce last year having endured a lengthy spell on the sidelines with a serious knee injury.
The 28-year-old spent time on trial at Tottenham Hotspur in January, with Arsenal believed to have considered offering the midfielder a deal while Cesc Fabregas was injured and West Ham were also linked with the player.
However, nothing ever materialised.
And Akunnor, who coaches Sekondi Elevise Wise, believes the former Juventus and Parma man needs to be playing regularly at a high level in order to be able to assist his country's 2010 World Cup qualifying campaign.
"I find it hard to believe," he said in All Sports. "In my days at the national team, there was no way you could play in the Black Stars when you are clubless.
"I know Ghanaians believe in him just as I also believe in him. But I will urge him to keep himself by finding a club as early as possible."
Appiah was last seen on trial at Russian champions Rubin Kazan, where a deal again failed to emerge.
And the midfielder was keen to bat back suggestions that clubs were being put off by both his wage demands and fitness following his long injury layoff.
“I went to England as everyone knows and trained with Tottenham for about four weeks,” he told his personal website.
“I was supposed to be there for a week, but it got extended for various reasons. Then I had another offer from the Russian champions, Rubin Kazan, and started talking to them, but that did not materialise.
“I can definitely say that it wasn’t about my wage demands and both clubs will confirm that. I wasn’t demanding what has been stated in some quarters of the media.
“My fitness levels were good given that I have been injured and out of the game for over 18 months. However, those deals with Tottenham and Rubin didn’t materialise and I have to move on.
“The future still looks good. I will be carrying on with my training as usual. I will also be training hard so that, if the Black Stars call on me, I will be ready.”
NEWS: Appiah linked with another London club
NEWS: Spurs to decide on Stephen Appiah signing
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