Manchester City have turned down an offer of €80m (£70.7m) for their winger Leroy Sané from Bayern Munich. The German champions are keen to sign the 23-year-old with two wide players, Arjen Robben and Franck Ribéry, leaving this summer and will now consider whether they are to make a new, improved bid.

The Germany international did not command a regular starting place in the City team last season but the manager, Pep Guardiola, is keen to keep him. The Spaniard said after the FA Cup final, which City won 6-0 against Watford to complete a domestic treble: “We offered to extend his contract. We want him to stay. What proof is more than for six, seven months we want to extend his contract? If we don’t want him, we don’t extend his contract.”

“Some movements we have to do for next season, because people want to leave, players want to play,” Guardiola added. “They accept not playing for a period but it’s normal that they want to play more. I can’t assure that to anyone so I understand completely.”

Last week the Bayern Munich chairman, Karl-Heinz Rummenigge, confirmed that Bayern are hoping to sign Sané. “We will try. I can not promise whether it will succeed,” Rummenigge said. “We already had the idea when he was still with Schalke, but at that time we did not have a guaranteed regular place for him. Robben and Ribéry were top of the top three years ago.”

Bayern won the Bundesliga by two points before Borussia Dortmund – and completed the double by beating RB Leipzig in the Cup final – but crashed out against Liverpool in the Champions League at the last-16 stage and it has been clear for some time that the squad needs rebuilding.

While City want to keep hold of Sané they also feel they have enough cover in wide areas – in Ryiad Mahrez, Bernardo Silva and Raheem Sterling in those positions – to cope with the Germany international leaving, should Bayern make an offer they cannot refuse and the player agreeing to the move.