Chelsea's pursuit of a striker to add to their forward options has led the reigning European champions and Europa League winners to lodge an inquiry with Galatasaray about the availability of their Turkey international Burak Yilmaz.

Yilmaz, whose career has taken in spells at Besiktas, Fenerbahce and Trabzonspor, has enjoyed an impressive first year with Galatasaray and registered eight goals in this season's Champions League. That haul included a winner against Manchester United in November, a hat-trick in Cluj and goals in both legs of the knockout-round victory over Schalke.

Chelsea, who should confirm the reappointment of José Mourinho as manager by the middle of next month, contacted Galatasaray to discover whether the 27-year-old was available. They were informed it would take a bid in excess of £20m to prise away the forward, who signed a four-year deal with an option for a further season when joining from Trabzonspor last summer. He had scored 33 goals in 34 league games for Trabzonspor the previous season.

That fee may prove prohibitive for a player who has not played for a club outside Turkey, even if he comes highly regarded by the former Chelsea striker Didier Drogba, who is a team-mate at Galatasaray.

Yet Chelsea's other options in the market appear relatively limited. Their long-standing target, Radamel Falcao, may yet opt for a move to Monaco, having indicated he will leave Atlético Madrid this summer, while Edinson Cavani is attracting interest from Manchester City. Robert Lewandowski, the prolific Borussia Dortmund forward, is expected to join Mario Götze at Bayern Munich after Saturday's Champions League final between the clubs.

Chelsea are seeking another established forward to compete with Fernando Torres, Demba Ba and, possibly, Romelu Lukaku next season. The young Belgian may be loaned out again to a rival Premier League club who are competing in European competition – Swansea have been mooted – to gain further experience after a successful arrangement at West Bromwich Albion last season.

Mourinho witnessed Yilmaz first-hand in the first leg of Real's Champions League quarter-final at the Bernabéu – the Turk was booked and missed the second leg through suspension – and will liaise with Chelsea's recruitment and scouting department over potential targets.

Yilmaz, whose 24 league goals helped secure the Turkish league title, has indicated a willingness to stay in Istanbul, though the ultimate decision over his future would remain with Galatasaray. "I'm really happy here," he said this month. "I have a long-term contract here. If an offer is put on the table then it's the club's decision which will matter, not mine."