The outgoing director general of the Institute of Directors (IoD) could soon be joining the board of the new International Trade ministry.
According to Sky News, Walker was approached about becoming a non-executive director for the department for international trade, a new Whitehall department established by the Prime Minister, with Liam Fox at the helm.
Walker is expected to agree to the role in the next few weeks, though he has not yet confirmed the approach. Sky reported that friends of Walker said he was keen to contribute to the UK's post-Brexit economy after he steps down as the head of the IoD.
A spokesperson for the department of international trade said: "In our search, we considered many attributes including experience in trade policy, proven leadership in large and complex organisations, leading major projects, an understanding of public sector challenges and a proven ability to contribute and inspire confidence with a range of stakeholders. The recruitment process is ongoing so we are not in a position to confirm any non-executive appointments at this time."
The IoD director general is due to step down next year after six years in the post.
When speaking at the IoD's annual conference last month, Walker took the opportunity to wryly reflect on Liam Fox's comments that British business executives were more focused on playing golf on Friday afternoons than in building the country's export base.
Fox had said, "We've got to change the culture in our country. People have got to stop thinking about exporting as an opportunity and start thinking about it as a duty - companies who could be contributing to our national prosperity but choose not to because it might be too difficult, or too time-consuming, or because they can't play golf on a Friday afternoon."
The comments did not go down well with the business community.
Walker said: "I would not have used Mr Fox's words about businessmen playing golf on Friday afternoons," though he did agree with aspects of the trade secretary's speech, such as the power of free trade and enterprise to reduce poverty.
Last week, more than 50 Labour MPs signed a letter demanding international trade secretary Fox outline any rationale for taking the UK out of the EU's customs union. He has previously hinted that future customs union membership is unlikely.