The Government also says security costs for visiting speakers must not be passed on to student societies.
The tabled amendments call for UK higher education institutions to report any financial arrangements they have with individuals or organisations overseas “to ensure that UK values cannot be compromised”.
Universities and student societies will also have to share details of overseas funding from specified countries, and would face fines or other sanctions over perceived risks to freedom of speech or academic freedom because of their funding routes.
The proposed threshold for reporting is £75,000, and will exempt countries such as Japan and Australia, listed in the Academic Technology Approval Scheme, as well as countries in the European Union and Nato.
The Department for Education opened applications on Monday for its new director for freedom of speech and academic freedom on the board of the Office for Students.
The director will have the power to sanction universities over cases of no-platforming or unlawfully restricting free speech.
Higher and further education minister Michelle Donelan said: “We are home to some of the best universities in the world and for decades students have travelled thousands of miles across the globe to study here because of our values of free speech and academic freedom.
“It is right that we are taking new action to protect our universities from undue foreign influences that work against British values – this is a Bill that the rest of the world will take note of.”
She added that she looked forward to working with the new director “to tackle these important issues and ensure we remain one of the most academically free countries in the world”.
The Commons will also debate a further amendment to the Bill on Monday to make sure security costs for visiting speakers at universities are not passed on to student societies, to prevent “no-platforming by the back door”.
The amendment says that security costs should be covered by the relevant body, rather than being passed on to societies or event organisers.
The Government said that this amendment followed cases where a student society at Bristol University had faced a £500 security charge from the student union to invite the Israeli ambassador to give a talk, while reportedly charging nothing for his Palestinian counterpart to speak.
The Union of Jewish Students has reported that some Jewish societies have been billed for security costs for a stall at student fairs.
Amendments will also set out that the legislation must include students’ unions at individual colleges, known as junior or middle common rooms, for example those based within colleges at Oxford and Cambridge.
On Friday, Tory MP Alicia Kearns warned that the Chinese government held too much sway over UK universities, adding that “education is being weaponised by those against us”.
She said that Confucius Institutes – public language and cultural education programmes funded by an organisation linked to the Chinese government – were “undermining the integrity of the Mandarin education in our country”.