Manchester City have made Leroy Sané, the highly rated 19-year-old Schalke forward, a prime transfer target but would hope to pay less than the €40m (£32m) the German club are holding out for.

City have been monitoring Sané since December 2013 and have now stepped up their interest. Txiki Begiristain, the sporting director, would hope to seal the transfer in January but the summer is considered a more realistic prospect.

Sané is contracted to Schalke until June 2019 after signing fresh terms in July, putting the German club in a strong position with regard to any bargaining. Horst Heldt, Schalke’s general manager, said on Wednesday that they will resist any approaches for the player who has scored four times in the Bundesliga this season.

“We don’t want to sell him and Leroy doesn’t want to leave the club,” Heldt told the German newspaper Bild. “Even Man City haven’t got that much money.”

In August Manchester United paid an initial £36m, which could rise to £58m, to Monaco for Anthony Martial, who was then also 19. So Schalke’s £32m valuation of Sané, who recently became a senior Germany international and who can break games open in a similar fashion to Martial, reflects the market price for a young footballer who is considered an outstanding talent but is yet to establish himself among the elite.

Sané made his international debut in November in the 2-0 defeat by France at the Stade de France. “Leroy has an incredibly good feeling when it comes to running into space and, with his speed, he has acquired this very well,” the Germany manager, Joachim Löw, said in the buildup. “He has shown the quality that he has in the final third and in the Bundesliga matches that we have observed, he has simply convinced us.

“He is a player with a special gift and finesse, speed paired with technique and strong running – at just 19. He can make the jump with us very quickly.”

The son of a former Senegal international striker, Sané was at SG Wattenschied 09 as a youngster before he moved to Schalke for a first spell in 2005. He left for Bayer Leverkusen three years later but returned in 2011 and made his first-team debut in a 3-1 defeat at Stuttgart on 20 April 2014. He has also played in the Champions League for Schalke, scoring a wonderful goal against Real Madrid in the 4-3 win at the Bernabéu.

City already have an abundance of attacking players, including the expensive summer signings Kevin De Bruyne and Raheem Sterling, but the club will always be in the market for the best young talent. The manager, Manuel Pellegrini, also has players such as Sergio Agüero, Wilfried Bony, David Silva, Samir Nasri, Jesús Navas, Patrick Roberts and Kelechi Iheanacho at his disposal but one or two of those may well leave in the summer.

Considering Sané is likely to cost at least £25m only a few clubs would be able to afford to sign him. Real Madrid are among those and they too have been scouting him extensively. There have also been reports that Liverpool are interested in the player and his team-mate Joël Matip. Manuel Pellegrini said on Wednesday that he feels his squad has sufficient depth but did not rule out strengthening in the winter window. “No, really I think the squad is complete. As always I said that we are not going to close the window but we are not really thinking of any special players to bring in.”

Of City’s reported interest in Real Madrid’s Isco, whom Pellegrini coached when in charge of Málaga, he said: “I always answer the same for that question. I don’t talk about rumours. I am telling you what I am thinking about for our squad in this moment.”

Pellegrini believes City’s problematic away form will be solved once his players’ finishing improves, with his team having taken three points from the past 18 available on the road. City have failed to win away since Crystal Palace were defeated by a late Kelechi Iheanacho strike on 12 September. At Leicester City on Tuesday they drew 0-0 when a number of chances were spurned, including a clear opportunity for Sergio Agüero after the break.

City are at Watford for Saturday’s late kick-off and Pellegrini said: “Maybe we have to finish a little bit more [calmly] and improve the important amount of offensive moments we have but I think we are in the correct way. If we didn’t win the last games that we play away, it is because we must improve.

“It was good to have a clean sheet [at Leicester] but for me the best thing from that game was to continue playing the same way we did in the last two games. We didn’t win against Arsenal but I think we didn’t play a bad game. We played very well against Sunderland and I think we played very well also against Leicester.”

Vincent Kompany suffered another calf injury when coming on as a substitute in the 4-1 victory over Sunderland on Boxing Day. The captain lasted only nine minutes before having to go off. City will again look at every aspect of Kompany’s mental and physical regime to try to find a final solution to his continuing muscle problems.

“We are trying to do all we can to know how we can help Vincent to try to be fit and not to continue with the same calf problems. So everything the club can do we are going to do it.”