It is understood that government officials will meet to discuss the move today, after a recommendation based on data showing rising cases in the borough.
If the move is approved then the measures could be announced by the government in parliament as early as tomorrow.
The number of cases in Telford has risen sharply over recent days, with 361 in the seven days up to October 22, giving the borough a rate of 200.7 cases per 100,000 people.
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One of the triggers for being moved up a tier in the government's system is have a case rate above 100 in 100,000 – along with other factors such as the level of hospital admissions.
Shropshire has also seen a rise in cases with the rate at 106.8 in the seven days up to October 22. There were 345 cases in the week up to October 22, 71 more than the previous week.
Both the Shropshire and Telford boroughs are currently in the tier one 'medium' risk category, meaning people can mix with other households inside or outside so long as the group has six people or fewer.
If Telford & Wrekin is moved in to Tier 2, people in the borough will no longer be able to meet socially indoors with others if they do not live with them – whether in private homes, pubs or restaurants.
People in support bubbles can go on meeting as before, and informal childcare may also be provided, and people will still be able to meet outside while adhering to the rule of six.
Schools and universities remain open under the rules, as do businesses but pubs and restaurants must ensure that customers consume food and drink only while seated, and close between 10pm and 5am.
The Department of Health has declined to comment on whether the issue is under discussion and only said that decisions in changes are taken after talks with local politicians and public health experts.
A government spokesperson said: “The Covid Alert Levels simplify and strengthen rules to help protect lives and reduce the transmission of the virus, whilst minimising the impact to livelihoods and the economy.
“Decisions are made in close consultation with local leaders and public health experts, informed by the latest evidence from the JBC and NHS Test and Trace, PHE and the Chief Medical Officer for England.
“We constantly review the evidence and discuss measures with local Directors of Public Health and local authorities, and will take swift action where necessary.”