Stephen Kenny says an approach to Patrick Bamford is "unrealistic".
The Leeds United striker wasn't named in Gareth Southgate's 33-man provisional squad for Euro 2020, and obviously wasn't in contention for the final 26.
An Irish-born grandparent makes Bamford eligible to play for the Republic of Ireland.
Having been capped at underage level for England, his lack of senior appearances fuel the continued talk of a potential switch to Ireland.
Speaking in March, Kenny hinted that an existing relationship between Bamford and a member of his backroom staff could work to convince the 27-year old to cross the Irish Sea.
"He has a relationship with Damien Doyle, our fitness coach," Kenny said at the time, "They were together at MK Dons for a while.
“Damien had been speaking to him, just chatting to him and at that stage he said he wouldn’t like to stand in the way of another Irishman."
Speaking ahead of the friendly with Andorra, Kenny was again asked if he'd be tempted to make a fresh approach to a striker who found the net 17 times in the Premier League this season.
"He was very close to being in the scheme of things... in contention maybe for England for the European Championships, so it's not realistic to suggest that now at the moment," Kenny said.
"I think that was obviously his objective - to go to the European Championships with England.
"There's no doubt he's a very good player. He's a quality centre-forward, but we have to believe in the talent that we have, and we have to work to improve it and get better.
"It's unusual for players to switch nationality - I'm not saying it never happens - but so quickly after... being left out a tournament. There's not many incidents of that, normally it's over a longer period."
Asked if he feels the England snub would change Bamford's way of thinking, Kenny said, "I really don't know.
"He is a good player, but his objective was clearly to play for England so we have to respect that."