Austria have to wait to call Barnes
Foda was at the London Stadium on Saturday to watch Barnes score the opener and have a hand in the second for Chris Wood in a 3-0 win.
But, ahead of friendlies with Slovenia and Luxembourg later this month, he is unable to add him to his squad as Barnes doesn't hold an Austrian passport.
Barnes qualifies for Austria through a grandparent, and represented Austria at Under 20 level 10 years ago, with a permit granted by FIFA.
Foda told Sky in Austria: "I went to see him against West Ham at the weekend for the first time. He did a really good job by scoring a goal.
"Me and my staff were impressed. He can use either foot, is physically very present and makes a lot of good runs. He was also involved in every single offensive play. What can I say, he is a very good striker.
"It was very important for me to see him live in the flesh to judge his competitive quality. Now, there are many other details to be discussed. Is he eligible to play for Austria? When can I involve him in my plans? We will see, what the next weeks may bring.
"I talked to people about Barnes. There are several Austrian players in the Premier League. The feedback was very positive."