Bayer Leverkusen midfielder Kai Havertz would consider a move to a club who have not qualified for next season’s Champions League.
The 21-year-old Germany international wants to leave the Bundesliga club this summer and has been linked with Chelsea and Real Madrid.
Although he wants to play in Europe’s elite competition, it is not thought to be a deal-breaker for any move.
Havertz considers a club’s long-term plan just as important.
Chelsea, who host Norwich on Tuesday, are third in the Premier League but lead fourth-placed Leicester and fifth-placed Manchester United by one point.
Only the top four will qualify for the Champions League next season after Manchester City’s European ban was lifted on Monday.
Last month Chelsea boss Frank Lampard described Havertz as a “top player” but said “no bids have gone in”.
Havertz, who can also play as a forward, has two years left on his contract and scored 17 goals in 43 appearances for Leverkusen this season.
That total includes seven in the nine games after the Bundesliga season restarted.
His team finished fifth – missing out on a Champions League place – and were beaten by Bayern Munich in the German Cup final.
But they hold a 3-1 advantage over Rangers after the first leg of their last-16 tie in the Europa League, which is set to be played to a conclusion in August.
Havertz has scored once in seven appearances for the national side.
Chelsea have already signed RB Leipzig and Germany striker Timo Werner for a reported £47m this summer.
Former Ajax winger Hakim Ziyech has also started training at Chelsea after his £33m move.