In-form Sterling was on target again, for the ninth time this season in City colours, as the champions overcame Bournemouth 3-1 in the Premier League on Saturday.
The 23-year-old, who extended his contract at the Etihad Stadium to 2023 last month, scored 23 times last term but Silva wants the England forward to better that.
bernardo Silva is confident that Raheem Sterling can keep on improving for Manchester City
The Portugal international said: ‘I hope he can get more than he got last season. He has been in fantastic form.
‘He is so aggressive with the ball and so focused on the goal. If he continues like this he will help us win some titles.’
Silva, who scored City’s first goal on his return from injury, also feels the team as a whole are improving and should be striving to set yet more records.
City won the Premier League last season with 100 points, 32 wins and 106 goals – all records.
Silva said: ‘It’s almost the same squad with some improvements, like Riyad (Mahrez), and more time together.
‘So, yes, we might be a bit better. We want to break the records of last season, but it’s not easy.’
Sterling scored his eighth goal of the season to help Manchester City to victory
Sterling’s goal was also his eighth in seven games versus Bournemouth for City while he also netted twice against them in a cup match for Liverpool in 2014.
The 57th-minute strike, moments after hitting the post, put City back in charge after the battling Cherries had responded to Silva’s opener with a deserved Callum Wilson equaliser.
Bournemouth felt they should have had a penalty for a Fernandinho push on Tyrone Mings but Ilkay Gundogan wrapped up the points for City, who were without Sergio Aguero, 11 minutes from time.
Silva said: ‘It was not an easy game. We knew we were playing a strong side and after our first goal we didn’t play as well as usual. We weren’t as aggressive defensively or offensively.
‘But the reaction in the second half was very good and we’re happy with the points and the win.’
Bournemouth felt they deserved a penalty for Fernandinho’s push on Tyrone Mings
Bournemouth slipped to ninth in the table after a fourth successive defeat but the mood at the club remains optimistic.
Defender Mings, who was recalled for his first league start of the season, said: ‘If you look at the spirit of the group – that’s a massive thing.
‘I think the manager’s tactics gave us a platform to compete with them.
‘We were in the game for large periods so we are walking away slightly disappointed to have conceded three goals to three things we had worked on.’