The 21-year-old has been between the sticks on trial for Telford during their last two pre-season clashes against Wrexham and Solihull Moors.
Addai, a former Arsenal youngster, has also been training with the New Bucks Head club.
Telford welcome League One Coventry tomorrow – where Addai is unlikely to feature – alongside the club’s open day and fans’ forum.
“We’re just having a look at him after hearing good things,” said Cowan.
“He’s looked good and will continue to be with us. We’re acclimatising him into the group. He’s still their player with another year left on his deal, we’ll know more in a couple of weeks.”
Telford are also running the rule over Tyrell McFarlane, a defender or midfielder, who impressed while with Market Drayton Town last tern.
Defender Keith Lowe, however, will not be staying at Telford after making an appearance as a trialist.
The experienced defender, 33, left Macclesfield in the summer and featured for the Bucks against Wrexham.
But the former Wolves stopper is expected to sign for another club.